Any history on the tractor?
When did this start?
Anything done made any difference?
Backfiring is typically an ignition issue.
Double check the firing order, just to say you did. Has the distributor been out or turned? If so check the ignition timing. Compare the old cap and rotor carefully with the new ones. Very common for aftermarket parts to be made wrong or misboxed.
Check the spark at each plug. The plug end of the wire, not at the cap. You can make a spark tester with an old plug, just bend the electrode back or break it off. Use the test plug to check spark at each wire.
Be sure the battery is fully charged. Connect the plug to a wire, lay the base against a metal surface, crank he engine and watch the spark. It should give a blue hot spark each time that wire fires. Check each wire to be sure all are firing.
Revisit the distributor. Be sure the points are properly adjusted and installed. Check the distributor shaft for side play. If there is side play, the points won't stay set.
Look the wire connections over, be sure the primary wire is securely connected to the points and coil, that it is not shorted to ground. Be sure the condenser is tightly secured to the breaker plate. Try an old condenser, they are commonly bad new out of the box.
If you have a test light, connect it from the - terminal of the coil to ground. Turn the ignition on. When the points are closed, the light should be off, open the light on. Play with the points, opening and closing, crank the engine, watch the light flash. If the light does not always respond, or flash when cranking, the points are not functioning properly.
Move the test light to the + terminal of the coil. It should light any time the ignition is on. If it goes out anytime, as in when cranking, or moving the ignition switch, the switch could be bad or a bad connection. It may dim when the points are closed. That is normal if there is a resistor in line, but it should never flicker or go completely off.
If all that checks out, move on to the fuel system.
A quick test: Remove the air filter hose from the carb. Remove the coil wire from the distributor cap and ground it. Hold your hand tightly over the air inlet of the carb, have an assistant crank the engine through. You should feel a strong, steady vacuum, nad your hand wet with gas.
If little vacuum, or pressure back, there is a valve problem or major vacuum leak.
If vacuum and no gas, there is a fuel delivery problem.
Next check the fuel availability. With the fuel valve on, engine off, gas cap loose, remove the drain plug from the carb, be ready to catch the flow in a clean glass. It should full flow, then slow to a trickle, but not a drip or stop.
Even though you have been through the fuel system, go ahead and do the test. There could still be a blockage, some sediment that was missed, a dirty screen, anything is possible, it happens.
Look at what was caught. If it's not clean, some residue may have made it through to the carb. It may need to come apart again and be cleaned out. You can ease it apart without needing new gaskets.
And then there are the obscure things to look for, clogged air intake, as in mouse nests, dirt dobbers, clogged mesh.
Valve problems, stuck, sticking valves, bent pushrod, broken valve spring, tight valves, flat cam... Run a compression test, visual inspection, set the valves.
Clogged exhaust. Rare but usually it will idle but not accelerate.
Let us know, we'll find it eventually!
