I have a leaky faucet problem and I am trying to replace the cartridge from the hot side that is causing it, but when I unscrewed the handle, I find that the cartridge is firmly put into it and I've tried using a wrench to unscrew it, but it's not working. I am not sure where to go from here and what to do to. It doesn't appear to me that there is any nut in there that I could remove. Any help would be appreciated it. Thank you so much. Here is a picture:
That chrome piece with the hex shape on top is definitely a retainer cap which needs to be unscrewed to access the valve/cartridge unit under it. You will need a bigger/better wrench perhaps. I always start by soaking stuck parts with penetrating lube/oil for a while (I use Liquid Wrench but there are a bunch of products out there.
There are specialized plumbing sockets that might allow you to get more leverage on that thin hexed part, like this: