Small Engines (Lawn Mowers, etc.): Troy-Bilt LTX-1842 Lawn Tractor w/18H B&S Engine - Backfires, soleniod, engine cutoff

Question
Last season my lawn tractor started backfiring to the point of engine cutoff.  I put it away to mess with it in the spring.  It's spring.  The same thing happened.  Exhaust was coming from the muffler (where the exhaust pipe enters).  I'm not an engine guy, but I think I can handle the work as long as I don't have to get into the engine. when I took the muffler off it was still smoking pretty good.  It actually surprised me how smokey it was. Any ideas of causes and solutions?  Thanks so much for any help.

Answer
Tom
What you have wrong is the Solenoid under the fuel bowl. What that is  called is a anti-backfiring solenoid,it shuts off the fuel to prevent fuel build up in the carb after you shut it off so it doesn't back fire or puff smoke out of the exhaust.Either a wire came off or the soleniod is bad.This part is easy to fix and replace.
Thanks