I am replacing the fuel tank assy and purge bulb (i.e. primer) on my Sears Craftsman model 358.798940. The original plastic tubing was old and brittle and broke apart while disassembling, so I could not tell how the tubing was routed. The new fuel tank comes with two lines -- one fuel supply w/filter, and a second line (probably for fuel return). I presume that I hook these up to the carbuerator (which has two fittings) -- correct? The purge bulb has two fittings for plastic tubing -- where are these routed?

there is a filter attached in the tank

The small diameter line out of fuel tank (has filter in-tank on end) connects directly to the side of the carburetor that has the fuel pump....that is the cover without the hole in it. Other larger diameter fuel line out of tank connects to the longer nipple on the external purge/primer bulb. The bulb "pulls" fresh fuel from the fuel tank to the carb and then out of the carb to itself, where it then "pushes" any air/old fuel back into the fuel tank. The remaining larger diameter fuel line in this setup goes from the metering chamber (has cover with writing on it and a vent-hole) side of the carburetor to the smaller nipple on the purge/primer bulb. Again, on the primer bulb, the longer nipple has a line going directly from it to the tank. This is the return line. The shorter nipple on the bub has a line from it going to the metering chamber side of the carb. If the purge/primer bulb is on top of the carb...small line from carb body to small hole in tank with filter. Larger diameter line goes from the bulb on the fuel pump side of the carb to the larger hole in the fuel tank where sometimes the line is held in place with a nylon nipple connector that keeps the line from pulling out of the tank. Otherwise, the line should enter the tank for about 1/2" or so

They don't really have fuel line routing diagrams available. This is even true on the Sears website. What they do have is the machine breakdown diagrams with all the parts listed and pricing for all available parts. I can give you fuel line instructions for a 32cc trimmer. I see that your model is a 24cc 2-stroke engine. This may point you in the right direction.
The small diameter line out of fuel tank (has filter in-tank on end) connects directly to the side of the carburetor that has the fuel pump....that is the cover without the hole in it. Other larger diameter fuel line out of tank connects to the longer nipple on the external purge/primer bulb. The bulb "pulls" fresh fuel from the fuel tank to the carb and then out of the carb to itself, where it then "pushes" any air/old fuel back into the fuel tank. The remaining larger diameter fuel line in this setup goes from the metering chamber (has cover with writing on it and a vent-hole) side of the carburetor to the smaller nipple on the purge/primer bulb. Again, on the primer bulb, the longer nipple has a line going directly from it to the tank. This is the return line. The shorter nipple on the bub has a line from it going to the metering chamber side of the carb. If the purge/primer bulb is on top of the carb...small line from carb body to small hole in tank with filter. Larger diameter line goes from the bulb on the fuel pump side of the carb to the larger hole in the fuel tank where sometimes the line is held in place with a nylon nipple connector that keeps the line from pulling out of the tank. Otherwise, the line should enter the tank for about 1/2" or so.

I see that this machine has a 2 stroke engine. These directions work on the 2-stroke engines of Sears trimmers. I've never seen a diagram but many explanations are out there.
The small diameter line out of fuel tank (has fuel filter in-tank on end) connects directly to the side of the carburetor that has the fuel pump....that is the cover without the hole in it. Other larger diameter fuel line out of tank connects to the longer nipple on the external purge/primer bulb. The bulb "pulls" fresh fuel from the fuel tank to the carb and then out of the carb to itself, where it then pushes any air/old fuel back into the fuel tank. The remaining larger diameter fuel line in this setup goes from the metering chamber (has cover with writing on it and a vent-hole) side of the carburetor to the smaller nipple on the purge/primer bulb. Again, on the primer bulb, the longer nipple has a line going directly from it to the tank. The shorter nipple on the bub has a line from it going to the metering chamber side of the carburetor. If the purge/primer bulb is on top of the carb...small line from carb body to small hole in tank with filter. Larger diameter line goes from the bulb on the fuel pump side of the carb to the larger hole in the fuel tank where the line is held in place with a nylon nipple connector that keeps the line from pulling out of the tank.

The small diameter line out of fuel tank (has filter in-tank on end) connects to the side of the carburetor that has the fuel pump....that is the cover without the hole in it. Other larger diameter fuel line out of tank connects to the longer nipple on the external purge/primer bulb. The bulb "pulls" fresh fuel from the fuel tank to the carb and then out of the carb to itself, where it then pushes any air/old fuel back into the fuel tank. The remaining larger diameter fuel line in this setup goes from the metering chamber (has cover with writing on it and a vent-hole) side of the carburetor to the smaller nipple on the purge/primer bulb. Again, on the primer bulb, the longer nipple has a line going directly from it to the tank. The shorter nipple on the bub has a line from it going to the metering chamber side of the carb.If the purge/primer bulb is on top of the carb...small line from carb body to small hole in tank with filter. Larger diameter line goes from the bulb on the fuel pump side of the carb to the larger hole in the fuel tank where the line is held in place with a nylon nipple connector that keeps the line from pulling out of the tank

This is an ongoing issue for users, and rightfully so. Small diameter line out of fuel tank (has filter in-tank on end) connects to the side of the carburetor that has the fuel pump....that is the cover without the hole in it. Other larger diameter fuel line out of tank connects to the longer nipple on the external purge/primer bulb. The bulb "pulls" fresh fuel from the fuel tank to the carb and then out of the carb to itself, where it then pushes any air/old fuel back into the fuel tank. The remaining larger diameter fuel line in this setup goes from the metering chamber (has cover with writing on it and a vent-hole) side of the carburetor to the smaller nipple on the purge/primer bulb. Years ago on 2-stroke trimmers, primers were not even used,...you choked the carb with a slide lever and gravity let fuel enter the carb from above...a few pulls, a "pop"...slide it off of choke and away you went.
If the purge/primer bulb is on top of the carb...small line from carb body to small hole in tank with filter. Larger diameter line goes from the bulb on the fuel pump side of the carb to the larger hole in the fuel tank where the line is held in place with a nylon nipple connector that keeps the line from pulling out of the tank

This is an ongoing issue for users, and rightfully so. Small diameter line out of fuel tank (has filter in-tank on end) connects to the side of the carburetor that has the fuel pump....that is the cover without the hole in it. Other larger diameter fuel line out of tank connects to the longer nipple on the external purge/primer bulb. The bulb "pulls" fresh fuel from the fuel tank to the carb and then out of the carb to itself, where it then pushes any air/old fuel back into the fuel tank. The remaining larger diameter fuel line in this setup goes from the metering chamber (has cover with writing on it and a vent-hole) side of the carburetor to the smaller nipple on the purge/primer bulb. Years ago on 2-stroke trimmers, primers were not even used,...you choked the carb with a slide lever and gravity let fuel enter the carb from above...a few pulls, a "pop"...slide it off of choke and away you went.
If the purge/primer bulb is on top of the carb...small line from carb body to small hole in tank with filter. Larger diameter line goes from the bulb on the fuel pump side of the carb to the larger hole in the fuel tank where the line is held in place with a nylon nipple connector that keeps the line from pulling out of the tank.

Fuel filter in tank with line going directly to the fuel pump side of the carburetor This is the end of the carb with a solid cover. . This line should have length in it inside the tank where it can flop around and stay on the bottom to collect fuel. The other line in the tank should have one of the little connectors on it and can be right up to where the hole in the tank is to hold it there.. This line should connect to purge/primer bulb on the longer outlet nipple. Another fuel line should run from the metering chamber side of the carb (the end with the hole in the cover) to the purge/primer bulb with the shorter outlet nipple.
The purge bulb "pulls" fresh fuel out of the tank via a vacuum created after depressing the bulb and the fresh fuel flows completely thru the carb and any air or old fuel ahead of it are drawn to the purge bulb which then "pushes" this mixture back to the fuel tank.

It's easy to mess this up as I've done it in the past. If the unit has an external purge bulb, the fuel line from the fuel tank that has the fuel filter on it goes directly to the carburetor...near the part of the carb that holds the fuel pump and has the grooved cover (where an inbuilt purge bulb would be). The other line coming out of the fuel tank goes to the purge bulb. The side of the carburetor that has the diaphragm and metering lever cover has the line going to the purge bulb. Remember, this is not really a primer...the purge bulb pulls air and old fuel out of the carb and when it does this, fresh fuel flows into it...and then the bulb pushes that air and old fuel back into the fuel tank. Hope this helps.

The smaller diameter line (fuel supply) goes from the fuel tank (w/filter) to the carb body. Another larger line (purge line) goes from carb body to the right nipple on the primer bulb. Another large line (return line) goes from the left nipple of the primer bulb into the fuel tank. co0mpleting the purge circuit. This info pertains to my 2006 Craftsman 32cc with Zama carb.