There are a number of things that can lead to "backfiring" including valve issues, timing, carburation, intake leaks....as you can see it's difficult to diagnose.
The first thing that should be done is make sure the timing is correct, take a vacuum reading, and tell us under what conditions it's backfiring. Is it steady pedal, just when it starts, or turns off, or just when you give it gas etc. Is it backfiring out the carb or the exhaust?
Tell us about the motor. Is it stock, cam etc? All will play a potential part.
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