Using the 12-inch-wide plywood pieces, position the two 22 1/2-inch panels with their cut ends inside the sides of the 24-inch pieces, forming a square. These are the sides of the box.
Drive four evenly spaced flush trim wood screws through the outside of the 24-inch panels into the ends of the 22 1/2-inch panels at each corner, using a screw gun.
Lay the 3/4-by-24-by-24-inch panel on top of the square; it should fit flush with all the edges.
Attach the top panel by driving flush trim wood screws through the top into the top edges of the sides, spacing them every 3 to 6 inches.
Apply a coat of paint to the exposed surfaces of the assembled bench with a paintbrush. Allow the paint to dry 24 hours.
Lay out four carpet tiles over the top of the bench. Remove the adhesive backing and press them into place.