Car backfires only on one spark plug?

So my ford 390 has a backfire (but only on the drivers side tailpipe…). Except for when I remove spark plug number 6. Doing so makes the backfiring stop. Also, I notice that the exhaust on that side of the engine is cooler and not as loud as the exhaust pipe on the other side. The car idles fine, but when you put it in drive it wants to stall immediately. Reverse makes it idle rough and want to stall as well, but not as bad as putting it in drive. I was planning on rebuilding the car (edlebrock 4 barrel) but am now wondering if the real issue is the misfire, and not so much the carb. What should I do first to try to remedy this? Any thoughts?

Run a compression test. This is typical of a bad camshaft or valve problems.

First, swap that sparkplug around & see if the backfire also moves.

Maybe you have a valve not seating perfectly in that cylinder, an exhaust valve unless it is firing through the carburetor. You don't say how you removed it? The wire or the whole plug? Could be just a bad plug or wire.

Compression test or cylinder leak down test. Pull the valve cover and inspect the valve springs for #6 cylinder. By removing you mean dis connecting #6 plug wire? Check the distributor cap and rotor. You gave no year, model etc… So it's hard to help and be more thorough.

I think the issue is… Ford? Maybe.

You probably have two plug wires switched (incorrect firing order).

Do a compression test. I'd guess you have a burnt exhaust valve on that cylinder.