Can't insert the big Enter key back into my keyboard

Its a bit of a pain in the rear but you need to VERY CAREFULLY hook the stabilisers/wire guides into the little 'hinge' like things, then push it back in. You'd want to use a pair of tweezers or a toothpick for that. The trick is to let the guides hang off the key vertically down and just over the keyboard and very carefully push it in place.

Do not use force. Make sure everything aligns before putting it in. As long as the wire is hooked in place, everything will work smoothly ... unless the wire goes out of place. Also the little plastic hinges sometimes break, which makes it even more of a pain.

EDIT : I've added a SE approved red free hand circle version of your image that shows which guide is to be hooked in where