Under acceleration my engine misfires?

Replace the entire set of six wires. I never tried removing them so I don't know what to expect for the result of doing that. The 3.3 / 3.8L uses a coil pack with three ignition coils. When you disconnect one plug wire, you will kill two cylinders. Worse, those coils are capable of quite a lot of voltage and if it can't create a spark across both spark plugs, it's going to find a different path and that often leads to arcing internally. Arcing leaves a carbon track behind which promotes further arcing and misfires.

A burned valve can also cause a misfire but that isn't very common anymore. A compression test or a cylinder leakage test would confirm that. They don't typically cause a backfire but they will cause the engine to run smoothly at higher speeds.

Info for 3.8L shows number 3 and 6 both fire off the same coil. I'm not sure what you mean by coil output not the same as other? Maybe I looked at wrong engine size? Plugs and plug wires ok? Cylinder compression ok? Fuel injector?

What is the engine litre size? If distributor, how about cap--rotor--plugs-- plugwires? Those are maintenance issues. If the problem is spark issue? I've been hit many times by secondary voltage, didn't like it when I was young, still don't like it.

I looked at the 3.2L, shows coil on plug ignition. The flow chart isn't worth much unless you have a scanner that shows live engine data, look at freeze frame data. I'd start by comparing voltage to number 6 coil to the others. Without more info, all I can do is hunt and peck.

This is for a mercury cougar 3.8-- rear wheel drive.

A plug or wire or injector or even a weak cylinder. Any weakness shows up more under cold conditions. Use champion plugs. They seem to hold up longer if your going to replace them. You should have it looked at while running. If it has a miss, it may be more then just a plug.