You'll want to cut back the drywall to the middle of a stud on each side. If the drywall was installed horizontally, there will likely be a joint near 4' from the ceiling. It's a good idea to use this joint as one of your sides for a patch of this size. To make the replacement easier, get all the edges clean and square. If you used any existing joint for a side, knock down any of the joint compound to get close to the paper.
Get a replacement piece of drywall. Cut it to fit the opening. Drywall is cut by cutting the paper on one face with a utility knife, snapping it back, and cutting the paper on the back. Use a rasp to smooth the edge. Count on 1/8" - 1/4" gap all the way around, so reduce your measurements slightly or rasp the edges back until the piece fits. Note, tapered edges go on top and bottom when installing drywall horizontally and tapered edges should always be met against another tapered edge.
Install it with drywall screws about every 12" on the stud and 8" on the side joints. To screw it in, a "mushroom bit" can be purchased that's designed to stop after the screw is slightly countersunk. You don't want to tear the paper, if you do so, you'll need to put another screw in slightly above/below to ensure the load is carried. And you don't want the screws above the surface of the drywall, otherwise the joint compound (aka drywall mud) will not be smooth. Make sure to put a few extra screws on the adjacent drywall if it wasn't already a joint.
Next, get some premixed joint compound and a few joint knives, perhaps 6" and 12" wide. Use the narrow knife to make your first pass over all the joints. Cover the joints with a paper or mesh drywall tape, and then put another layer of compound on top and cover all the screw heads with a little joint compound, too. Allow to dry, smooth out any rough edges with a screen sander, and then cover the joints with a second layer of compound with your wide knife. You want to fan out the joint as far as possible (e.g. 12" from the joint to each side) to make the seam disappear. Allow to dry and lightly sand with a mesh screen once more.
Prime the patch with a good primer and find a matching paint (take a paint chip to have it color matched). I'd also paint the whole wall, but if you really need to save on effort, feather out your painting so that you can't see the contrast from new to old paint.