I have a cf 500 4x4 that has acceleration problems. as soon as I try to throttle up the engine starts to die. By holding my hand partly over the carby intake, I am able to increase the revs without any engine problems. Originally, I thought it was air cleaner problems but now I think it is more of a carburetor problem, Any ideas?

[2015 Z Force 800 53/Trail EPS]

I think these are fuel injected so no carbs. But it would appear you may have mor air then fuel and by cutting down the air it helps so check the fuel supply-both pressure and volume.

The older 500 did have a carb. Will it rev if you very slowly give it throttle? If you have to choke it with your hand, I would start with a carburetor cleaning. After that, look for air leaks in the intake boot or mounting surfaces. Poor fuel flow can also cause this. This is assuming it ran fine before and nothing on the carb has been messed with. Good flow, clean and no air leaks, move on to ignition and clutch issues.

I would guess at a blocked slow speed jet. Carb off and a good clean of all jets and passages should help.

Depending on the age, I would definitely make sure all of the carb boots are in good shape.  I've had machines do that due to a torn boot between the carb and the intake.  If not that, make sure the carb is clean.  Also check your oil to make sure you haven't filled the crank case with gas.  A leaking needle valve will allow gas to poor down into the crank case.  This will also cause the symptoms you are describing.