Outdoor Power Equipment and Small Engines - Briggs 18 twin backfires

Just got this tractor and it has just the engine I've been looking for. It didn't run to good so I completely tor down the carb and cleaned it, installed a fuel pump kit, changed the oil,... anyway now it runs great except for a loud backfire when I throttle down.

I thought it might have something to do with the muffler but I'm not sure.

When you throttle down OR shut down?

Throttling down to put it into idle. I always throttle down to idle before shutting it off. Another thing is it's only running smooth at half 1/4 to 1/2 choke which is a fuel delivery problem. I still have to replace the fuel filter, but could bad spark plugs do this?

Model: 422707
Type: 1264 01
code: 9412215B

Otherwise it starts quickly and runs smooth and strong.

Spark plugs would be noticeable throughout the RPM range, not just on idle down. Generally, a backfire, in this circumstance, is going to be a rich fuel condition whereas excess fuel delivery cannot be handled by the ignition and you get raw, unburned fuel into the hot muffler and the muffler burns it off and thus the backfire. But this goes against your situation since you have a lean condition since you have to run at part choke to get the engine to run well. I suppose a loose/rusted baffle in the muffler could produce a backfire-like sound.

Just thought of something...

Could the backfiring be caused by the engine running the little bit of carb cleaner left in the carburetor?

I doubt it, I think that any residual cleaner would clear out in a matter of minutes and any adverse performance would disappear relatively quickly. You didn't rebuild the carburetor and perhaps you should so as to ensure you have a good fuel delivery to the combustion chamber.