Place two of the pieces of 11 3/4-by-12 1/2-inch MDF on a worktable. Measure from one long edge and make marks at 1/2 and 1 1/4 inches. Put the framing square on the marks and draw lines parallel to the long edge. This indicates the placement of the front of the speaker box.
Make several marks 3/8-inch from the remaining three edges. Set the framing square on the marks and draw lines parallel to each side with the corresponding marks. Drill pilot holes on the lines with a 1/16-inch drill bit. Drill one about 1-inch from the ends of the lines and one in the center.
Drill pilot holes between the lines drawn on the front edge of the material. Drill countersink holes 3/8-inch deep with the countersink bit directly on the pilot holes.
Put the remaining two pieces of 11 3/4-by-12 1/2-inch MDF on the worktable. Measure from one long edge and make marks at 1/2 and 1 1/4-inches as you did before. Make marks 3/8-inch from the other long edge and draw lines connecting the marks as before. Drill pilot holes and countersink holes as well. These are the top and bottom of the speaker box.
Apply glue to the 11 3/4-inch ends of the top and bottom pieces. Place them between the other pieces of the same size. Secure them through the pilot holes with the drywall screws. Clean up the excess glue with a damp cloth.
Brush glue on the four edges of one of the 12 1/2-by-10 1/4-inch MDF with a small paintbrush. This is the back of the speaker box. Place it between the four pieces already assembled keeping it even with the outside edges of the four pieces. Secure it to the pieces through the pilot holes with the drywall screws. Clean up the glue as before.
Lay the other piece of 12 1/2-by-10 1/4-inch MDF on the worktable. Place the long leg of the framing square on diagonal corners and draw a line. Repeat this with the other two corners. This marks the center of the material. This is the front of the speaker box.
Set the compass on 4 5/8-inches to accommodate a 10-inch speaker. Stick the point of the compass on the lines where they intersect and draw a circle. Cut this out with the jigsaw. Brush glue on the four edges and secure the front through the pilot holes on the sides, top and bottom with the drywall screws. Install the jack plate in the desired location according to the manufacturer's instructions.