Here is my problem.

I have a 2008 honda accord EX-L V6 coupe. My AC compressor clutch will not engage. The relay clicks when I turn on the AC so I don't think it could be the relay. I replaced the compressor and that did not fix the issue. When I fill the system with coolant the fans kick in and the pressure rises past 150 psi on the low pressure side. Any idea on what could be the issue?

 

Also, a clicking relay doesn't mean the relay is actually working. You can try swapping the compressor relay with something identical nearby like the defrost relay. If the compressor works and the defrost doesn't then the relay is the problem.

You should also check the fuse for the a/c compressor. The 4-cylinder is a 7.5 amp fuse in the engine bay fuse box, but I don't have a V6 shop manual. I'd expect the setup to be similar. Look under the fuse box for a diagram of the fuse location. The owner's manual should have this information.

You will have to do electrical troubleshooting if the above steps don't work.