Drywall repair in bathroom.
The easiest DIY repair for this hole is go to the HD and in the paint dept there are patches in4" 6" and 8" sizes. They are square pieces of alum. with a fine mesh tape over then and they are sticky. While you are at the store pick up some sanding screen (in the drywall section) and a can of knockdown texture in a can (paint dept). Now sand all around the hole so the patch will sit flat then sand all the texture out about 5 or 6" from this area stick the patch over the hole then put on a thin coat of drywall mud allow that to dry then sand any ridges off and add a second coat going out past the edges of the first coat. Pay attention to where the mud and the existing drywall meet to get it as smooth as possible. At this point sand the texture out a little farther from the patch. Let dry sand, prime, texture, reprime then paint.