Pour some gasoline on it, and ignite it. It may remove more material than you want, but sacrifices have to be made...
Water based paint . . clean w. warm soap and water. Oil based paint . . your bummin. Try laquer thinner fresh white rags. Good luck. If all else fails just put some furniture over it.
try some sort of virgin solvent a little spot at a time. if you have to use a generous amount you will need some way to rinse the carpet out. be careful because the solvent can damage the fibers if you use to much
The trick is to get it off when the paint's still wet. The longer it has to dry and congeal on the carpet, the more difficult it is to remove it competely. If the paint was latex, you can soften it with Disolvit or an orange-based solvent, and blot it out with soapy water and paper towels. If the paint's oil based, you'll have to use turpensol. There may be some damage to the carpet; the dye may fade or the fibers fray, depending what the carpet's made of. Do a test on a small bit of unseen carpet with whatever solvent you try, to see if there's a lot of damage. You might have to call in a carpet cleaning professional.
by cutting that piece off and replacing it
