Hard starting & backfiring are one of the most common problems I see people ask about. It usually will be within the carb itself. Years of use, bad fuel, ethanol, dirt, buildup, etc. all will cause the tractor to start hard. The best thing to do, especially if nothing has ever been done to the carb, is to rebuild it. New needle and seat, float, completely cleaned inside & out. Next best thing, would be to replace the fuel lines going back to the gas tank. You'd be surprised how brittle and corroded a 20-30 year old gas line can be. And after doing all that, making sure the gas tank itself is flushed out. You'll then know, your fuel system is solid.
Rattosh51
YT6800