A carb out of adjustment can do it. Checking it is very quick and simple.
I'm pretty sure the carb on the D has two needle adjustments you can do by hand - a load needle and an idle needle. (should be marked on the carb - look closely).
Open the idle needle up a few clicks and see if it makes a difference. If not, go a little more. If you're blowing black smoke, you've gone too far And if it's still backfiring, put it back where it was and look elsewhere.
(if you get lost on where you're at with it, just crank it all the way in, then back out 1 1/2 turns and it should be good).
If you're still backfiring - I'd look at the plugs, and while they're out do a compression check on each cylinder.