alot of good advice on here, the best repair for a hole that size is (I agree with earlier posters) to cut it out and then use at least some 1x4 to frame the hole, or they also make a metal "flange" type to span 2 pieces of drywall, make sure the hole and the piece you are putting in are within 3/16" of each other or you will have a massive gap to fill, I suggest paper tape over the mesh kind of joint tape, but it's is all preference... if you use mesh put it on first then mud over the top of it... first coat should barely cover the mesh, light sand the edges after drying to smooth the patch down... use a low dust mud on the first coat (in a blue and grey tub at lowes) after you can use 20 min on the rest it'll save you time and you can finish quickly..... any more advice just call....