Measure an 8-by-8-inch square onto the drywall and mark it with a pencil. Cut the opening out with a keyhole saw. Discard the square of drywall.
Cut two 8-inch pieces and two 6-inch pieces of 1-by-2-inch board. Drill holes in each board, inches from each end. Sand the boards with medium-grade sandpaper to remove any burrs or splinters.
Place the boards onto the wall, with the longer boards on the top edges of the square, surrounding the opening, and mark the location of the holes onto to wall. Remove the boards and drill holes in each of the marked locations. Insert a hollow wall anchor into each of the holes.
Drill two holes into the 8-inch boards, each hole 1 inch in from the ends of the board. Countersink the holes so they are large enough to accept the heads of the carriage bolts. Slide the bolts into the holes.
Place the 8-inch boards on the top and bottom edges of the opening, with the carriage bolts extending into the room. Fasten the boards to the wall with screws through the board and into the hollow wall anchors. Place the 6-inch boards on the vertical sides of the opening and secure them.
Cut a square piece of plywood, measuring 12 inches by 12 inches. Drill holes in the locations corresponding to the carriage bolts. Sand and paint the plywood to match the wall. To use the panel, slip it onto the carriage bolts and secure it in place with the wing nuts.