Drywall repair

I have a hole in a drywall wall to repair. It is about 2 inches wide and about 6 inches long. The drywall is 5/8th thickness. Is the best way to repair it, to fill the hole with mud and then put drywall tape over it? Then sand and add more mud as needed? Or should I try to put a piece of
drywall in the hole first?

Screw a stick to the inside of the hole to support the patch. Fill the hole with a scrap of dry wall and put a coat of mud over it to just fill the cracks. Remove the screws after the mud dries, the patch should hold on its own. Then continue mudding, with taping over the joints. If worse comes to worse, you can replace the whole piece. Sheetrock is cheap and relatively easy to work with. Just take your Milwaukee Sawzall and cut out the old piece to the studs. Then you can install a new piece and tape and float it.