My chain snapped and I fixed that. But exactly how is the chain threaded through the Shimano rear derailleur? What is the correct path over and under the 2 jockey wheels? I cannot find a diagram that shows me clearly how to do it. I believe that correcting my problem will involve taking the chain apart again and rethreading because when I try to peddle the chain is not feeding through properly to move the bike.

I had a look at the Mongoose website.
They have manual for download.

https://int.mongoose.com/pages/product-manuals

Enter the model of your bike, or look for a picture of it.
Follow the instructions....

REgards
Geoff

There is typically not a single cause or solution to a specific shifting problem. The most common way to resolve your problem is to let off a bit on pedal pressure as you shift. The derailleur has to move the chain sideways off the teeth, and that is more difficult when the chain is under high pressure.

I’m happy to help further over the phone at https://www.6ya.com/expert/donald_f2ed37026a3ac881

Try flushing out the shifter(s) with WD-40, use plenty. The next step will be replacing the shift cables and cable housings.

• Take the bicycle in an area free of cars and obstacles, such as an open parking lot. Concentration is required when learning to use Ultegra shifters or any other type of bicycle shifter.
  
• 2 Mount the bicycle and rest both hands on the proper Ultegra hand control. The left-hand control operates the front derailleur. The right-hand control operates the rear derailleur.
  
• 3 Start pedaling, smoothly and evenly. While pedaling is crucial to propelling the bicycle forward, it is also necessary when shifting the derailleur. Pedaling forces the chain to rotate. The chain must rotate before it can transfer to another gear.
  
• 4 Push the outside right Shimano Ultegra lever in toward the bicycle. The rear derailleur will shift the chain to a smaller rear gear.
  
• 5 Push the inside right Shimano Ultegra lever in toward the bicycle. The rear derailleur will shift the chain to a larger rear gear.
  

Rear Ultegra Derailleur Control

• 1 Push the outside left Shimano Ultegra lever in toward the bicycle. The front derailleur will shift the chain to larger front gear.
  
• 2 Push the inside left Shimano Ultegra lever in toward the bicycle. The front derailleur will shift the chain to a smaller front gear.
  
• 3 Use the front and rear Ultregra hand controls interchangeably. For small changes in gearing, using the rear control. For larger changes, choose the front control. A smaller gear causes the bicycle to travel a shorter distance per pedal stroke but also requires less energy to use. A larger gear requires greater effort but in turn causes the bicycle to travel farther per pedal stroke.
  

Snagging? Like hooking on the teeth in a bad way? Go through all the rear derailleur adjustments.

http://www.parktool.com/blog/repair-help/categories/derailleur-systems

Look for worn parts...

http://sheldonbrown.com/chains.html

Get out your wallet.

Web search "how to replace rear wheel on bicycle" for videos. We can't see it to assess.

The deraileur should have two screws on the right side (facing you when you look at the derailleur) try making the screws tighter or looser to tune the derailleur.

If you learn to shift correctly this won't happen..

Google bicycle shifting technique, for example:

http://coachlevi.com/cycling/complete-beginner-guide-to-bicycle-gears-shifting/

You should NEVER run cross-chained (big-big or small-small). The drive train performs best when the chainline is as close to straight as possible. Excess sideways stress on the chain will wear it out prematurely and increase its normal efficiency.

To demonstrate this for yourself, put the bike in the same combination of gears you're having a problem with. Get behind the bike and look staright along the top of the chain. As you can see the line of the chain is a mild zig-zag where it is parallel to the bike at each gear but needs to angle across the drivetrain in between. On some bikes the chain might even come in contact with the next larger chainring when used this way.


If you can shift to the big-big combination without snapping the rear derailleur off, you're lucky. The big-big combo uses up all available chain length and the rear derailleur will be pulled toward the front of the bike, sometimes so far that it is in danger of being snapped off.

THERE IS NO UPSIDE TO CROSS-CHAINING.

As you can see, the rear derailleur is not long enough to **** up all the slack this gear combination creates. There are other combinations that would yield the equivalent gear ratio without either stressing the drivetrain or dropping the chain.

The basics of shifting are these:
1) The big ring and right side of the cassette in back are for speed.
2) The small ring and the left side of the cassette are for high torque, lower speed

Have a look at this website:http://www.parktool.com/repair/byregion.asp?catid=5 I'd recommend Shimano or SRAM parts.

Here is a link to a tech sheet for a Shimano Deore rear derailleur. It is not your exact one, but all Shimano derailleurs are more or less the same. Make sure you have thoroughly cleaned your drivetrain with a degreaser (like Simple Green) and a brush to clear all grease and debris before making adjustments. The second step is to shift into your highest gear (the smalles cog) and then release the cable in the derailleur, pull taut and retighten it. Check again to make sure you can not get into low gear, because it may have been a problem with cable tension, which you just fixed. If it still does not, then adjust the "L" setting on the derailleur so that the jockey wheel on the derailleur will move just ever so slightly past the last cog on the cassette when the shifter is fully engaged.

Hope this helps,
matt

There are several things that could be wrong. You could have thrown your chain (you couldn't ride at all if so). The bike could have been crashed and the derailleur bent. The cable might have slipped where it bolts to the derailleur. Or the cable or shifter could need maintenance, too. It is most likely one of the above. If it is only the adjustment, there are two stop screws on the derailleur that can be adjusted.

My best advice for you is to either find a bicycle repair manual at a local bookstore or your library that can show you some of the detail. Or just let your local bike shop do the repair.