Place a 3/4-by-18-by-18-inch plywood board on the working surface. Set out two 3/4-by-6-by-18-inch plywood boards, resting them on their long, thin sides on top of the plywood board, which is the bottom board. Space these boards, which are the side boards, parallel to each other with their outside surfaces even with the edge of the bottom board.
Position 1-inch metal L-brackets against the bottom board and the side boards, spaced every 6 inches. Mark the screw attachment holes of each bracket against the bottom board and the side boards. Remove the brackets and drill out each hole, stopping the drill from drilling all the way through the boards. Reposition the brackets and attach them in place with 3/4-inch wood screws.
Flip the assembled unit upside down and set it on top of another 3/4-by-18-by-18-inch plywood board. Set brackets along the inside corner between this board, which is the top board, and the side boards in the same manner as before. Mark the position of each bracket and drill the holes. Attach the brackets to the unit with 3/4-inch wood screws.