Some potential cures for backfire occurring through a carburettor or a muffler are to change fuel brands or taking time to idle the engine to a neutral speed before shutting it down. Another cure could also be to check any attached anti-afterfire solenoid to see if operation has been compromised, as well as optimizing the carburettor itself to get the best performance.
A backfire occurs in the carburettor when a bang of audible sound occurs as the engine is being shut off or is in the process of idling down. This can be caused by a variety of reasons, including an engine being shut off while still at high RPM and using fuel that contains alcohol.
When a car engine is shut off at high RPM, fuel can still go through the engine and into the muffler, which can still be at a high temperature. This can cause the fuel to ignite and pop. Fuel that uses alcohol also ignites easier than fuel that does not, leading to higher engine temperatures and a higher potential for ignition. Sometimes the type of muffler installed by the car manufacturer or an improperly working anti-afterfire solenoid may also lead to a backfire occurring.