screws
I do not have much experience with home improvement related things. I moved into my first apartment and I saw that the internet coaxial cable was pushed inside the outlet. I loosened the screws and using a knife I cut the thin paint layer around the cover and removed the cover
I pulled the coax cable out and fixed the position but when I try to screw the cover back it won't go in. What do I need to fix this outlet cover?
There are several kinds of drywall anchors and they each have their own weight rating. Some work by drilling a small hole and tapping in a plastic sleeve and others work by drilling a bigger hole and screwing a plastic sleeve and there are others where you drill a hole and the metal butterfly expands behind the drywall know as molly bolts (thanks comments!). Recently I saw anchors where you drill a 1 inch hole in the drywall and this big contraption grips the inside of the drywall (wish I could remember the name). Anyway, each of the big drywall anchors could hold over 50 pounds!
The positive response got me to go dig for those contraptions. Turns out they are made by Moen and they're called SecureMount. I have the Moen SMA3000 and they really are just a bigger version of toggle bolts (spring loaded metal wings that fold and have a long machine screw).
I also found this useful link that has pictures and describes all the types mentioned (except the SecureMount of course . . . those are new and very much a niche product).
You have a few options available to you, based on the material which you find.
Provided that I understand how you want to assemble the structure you can do the following.
(see pics below)
Best Answer
Low voltage plates without brackets make for a sad DIYer
It appears the last installer tried simply screwing the cover plate to the drywall directly without a bracket or box to back it up. Unfortunately for them, screws don't hold well in drywall, as you found out the hard way. While you could use drywall anchors, there isn't much left there for them to hold on to, thanks to the screw-job chewing up the drywall.
It'd be better if you got something called an "old work low voltage bracket", such as the one shown below, that installs behind the drywall with a set of built-in clamps that hold it to the wall. You'd have to cut out the damaged drywall around the existing hole to the size of the bracket's cutout, insert the bracket, and then engage the clamps. Then you can screw the faceplate to the bracket and have things stay together properly. (Obviously, you need to undo the cable to do this.)