Plumbing Questions? Ask a Plumbing Expert.
Welcome to Just Answer. I will do my best to fully answer your question(s).
Is this a bathroom sink faucet?
Okay thank you. They can get limed up (hard water deposites and soap build up) underneath the threads over time making them a "bugger" at times.
Grabbing hold of the faucet base (bell or cup shaped portion) under the handle (as close to the sink as possible) try turning counter clockwise. It may help to have another set of hands holding the portion in place underneath the sink so it does not move. It you cannot turn it then next try a thin clothe to cover it and use a channel lock pliers. gentle with the teeth though so you don't scratch the finish.
Unfortunately you cannot get at the threads to apply some WD-40 to assist here. Just going to need some elbow grease.
If you can find your faucet on the kohler website
I may be able to help you more but the directions with be the same. If you wand to loosen it from underneath this will allow you to raise up the valve and maybe be able to get hold of the parts better with two wrenches. its difficult underneath, not alot of room to work. Worth a shot.