Probably time to rebuild the carb on that engine. Backfire can be a function of an off air/fuel mix, bad jets int eh carb, poor atomization of fuel, timing is off. or valvetrain is damaged. The 20R uses a timing chain that generally will last the life of the vehicle, but has to be checked every once an a while for chain stretch or worn chain guides. Also keep in mind that the 20R is an interference engine, meaning if the timing gets too far off or the timing chain breaks - you will probably end up destroying the valves/valvetrain/piston tops in the process.
First I would double check the timing, then the air/fuel mix. Try cleaning the carb first to get any deposits off then start thinking about getting it rebuilt.