I am installing the carpet in my '72 Chevelle. I got the front carpet in and I am now working on the back piece of carpet. This carpet comes in two pieces.
My question is: Do I need to cut a hole on the carpet to fit over the brackets that holds in the rear seat bottom? There are two brackets or groves or whatever that the rear seats fits into. I would assume that cutting a hole on the carpet to fix over the brackets would help the carpet not move.
Does this make any sense?

Yes, you need to cut around them, but be as precise as you can. You can see most of that area even after seat is installed.

Try and make slits more than cutting out a section.