Replacing the panel as mentioned above would probably give you your best results. If you decide to just patch the hole and paint, the patch will probably always be visible, although maybe not too bad. If the existing panels have any type of texture to is like tiny screen effect or wood grain, you will lose that texture when spackling up the repair.
When I repair a 6" hole like that, I will cut maybe 4 pieces of 1x2, 10" long and "button hole those into the hole. This will leave 2" of overlap to be able to fasten it with. I use a pneumatic stapler and glue, but screws can be used. Screws can be harder to smooth out if they do not countersink. They also have a tendency to split the 1x2. Using short screws that penetrate the 1x2 by only 1/2" can help. I will put as many of these 1x2 pieces in the hole as will fit. Holding the 1x2 vertically, you can put the ones on the outsides edges in by holding it with one hand while fastening it wiht the other. When you get to the 1x2s in the middle of the hole, where there is no room for your fingers, put a sheetrock screw in the middle of the 1x2 and use that to hold it in place while fastening it. Now you have a backing that you can attach your patch to. Get it all fastened. If you used glue, be sure it is dry before covering with spackle or paint. Sand it best as you can and paint.
That is how I would fix a hole in a wall. If the hole is caused by a doorknob, I might just cover the hole with a stained or painted piece of trimmed wood and put one of those rubber wall/door protectors on it.
Today is PERFECT!
All information and advice given is for entertainment and informational purposes only. The person doing the work is solely responsible to insure that their work complies with their local building code and OSHA safety regulations.