Why is my john deer riding mover backfiring and how do I stop it.

Inspect/replace the air filter to ensure proper air flow.
Inspect/replace the sparkplug(s) to ensure proper firing.
Check the position of the "choke" (if equipped; & by the way, most riding lawn mowers do not use a primer bulb button to prime the engine before starting).

Gas is bad these days. If it's turning over but not starting, Pull the plugs and replace, they are cheap. Drain the gas out and add high test with no ethanol. Add a couple drops of a fuel jet cleaner. Turn it over a couple times. Don't panic if it does not start leave it sit overnight, then start. Check the gas filter and air filter as well. Nothing here expensive. Unlikely anything else wrong unless someone was paying with the carburetor or choke.

if hdrostatic mover hydro going out

Please refer to this site for details on trouble shooting manuals. I am hoping you are after John Deere tractor lawn movers etc.

Troubleshooting

There are not of reasons for lawn mover starting and then dying.
Please see this John Deer site for possible causes and fixes.

Troubleshooting

I have not worked on these lawn mowers but there is plenty of posts on different lawn mower sites on how to rebuild the John Deere L1xx series transmissions. I would suggest have a read of this site. It also mentions the parts required and the cost. I understand these lawn movers use the K46 transmission system.

TuffTorq K46 Repair Guide with Pictures

Mine acted the same way. Found out I had lost a cylinder. I would check your compression before doing anything else.

are you loosing spark when it dies?are you loosing fuel ?

i have 14hp kawasaki that backfire throw the carb and exhaust what could it be

Of the 100+ camshaft replacements that I personly have done on the 425/445 and John Deere Gators I have come across 3 that backfired when completing the replacement.2 were do to bent valves coming in contact with the piston after gear failed and 1 was from a sheared flywheel key.The only other time I had this same injected engine backfire was on a John Deere gator 620i that had a faulty computer and fired @ 90 derees off.Do a compresion check and that will help out alot.