How or what is the choke hooked up ?

Are you sure is isn't 2046, rather than 2446?

Support here

https://www.snapper.com/na/en_us/support.html

But, you need Engine Support, not Snapper Support. This is an oddity with small garden appliances.

https://www.google.com/search?q=snapper+st2446-00+parts+schematic

Carburetor info

https://www.google.com/search?q=snapper+st2446-00+rebuild+carburetor&tbm=isch&ved=2ahUKEwiojbSc0I3xAhVPZKwKHZyaA7wQ2-cCegQIABAA&oq=snapper+st2446-00+rebuild+carburetor&gs_lcp=CgNpbWcQAzoECCMQJ1Cgtg1YirUOYL23DmgCcAB4AIABrQGIAfYTkgEEMjYuNJgBAKABAaoBC2d3cy13aXotaW1nwAEB&sclient=img&ei=rVDCYOiCJc_IsQWctY7gCw&rlz=1C1QJDB_enCA643CA644&safe=off

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1984 if I remember is a carburetor so you should have a throttle linkage return spring. Check to see it's not broke or stretched out, also check the choke return spring that that is not stuck.

I didn't think the choke had a spring on it. However, it does sound like a governor spring to me.

A model and serial would help

U need a service manual unless you know someone who knows what is what. Nest time you will take a picture in advance before you disassemble something.

The ends of both springs hook at the loop of the metal linkage connecting the governor vane and throttle shaft. The other end of the small spring hooks onto a small upright plate approximately 1 inch towards to the front of hooked end of the spring. The longer spring hooks onto a large hole in the throttle plate.
A problem that does occur is the plate becomes bent when the mower us pushed under shrubs. This drops the speed of the mower to a low idle. If this is the case then with a pair of pliers, gently twist that metal plate to obtain a RPM setting of 3,100. Don't be tempted to increase the revs to much or the conrod will break and punch a hole through the engine block.

Brent,
Most any auto parts store will have a manual choke conversion kit for about $10us.You will have to be a little creative to hook it up. But...your engine shouldn't need to be choked once it runs awhile and is still warm. I would look for other causes like binding linkages, unhooked springs and loose carburator mounting.

It would help to know the make, model, and HP of the engine. However, if the avatar shown is similar to your machine, here is a pic of the spring placement on the carb.



If this is the kind you have, you can easily see where the spring ends go. However, where the springs join to make a "V" is a bit obscure. They join to a loop in the hard link which connects the governor to the throttle plate.

Hope this helps.

**WARNING**
Make Sure the throttle moves freely. If the linkage becomes pinched your engine may run away and either become damaged, destroyed, or may even do harm.

Besides the service manual you can view parts diagrams at a dealer like www.arcolawn.com. You can purchase the service manual at a dealer and it will show you how to hook it up.
The throttle linkage hooks up to the throttle shaft closest to the engine. the governor spring attaches the governor arm to the throttle linkage.
The choke cable attaches to the shaft farthest from the engine. I hope this helps.
PS your engine has two factory service bulletins on it.
Joe

the little spring should go through same holes as the linkage it's purpose is to take the slack out of the rod to keep the engine running smooth a broken spring will cause it too run erratically