Measure the height, width and depth of the dishwasher using a tape measure. Add 4 inches to the depth, 2 inches to the height and 2 inches to the width to find the dimensions of the cabinet. Cut two pieces of 3/4-inch hardwood to the height and depth of the cabinet using a circular saw. Cut one piece of 3/4-inch hardwood to the width and height of the cabinet.
Cut one piece of 3/4-inch hardwood to the depth and width of the cabinet. Cut two pieces of 3/4-inch hardwood to a length equal to the width of the cabinet and a width of 2 inches. Cut two pieces of 3/4-inch hardwood to a length equal to the width of the cabinet and a width of 6 inches.
Apply wood glue to the end faces of the 6-inch and 2-inch wide pieces. Stand one of the cabinet height and depth pieces so the cabinet height edges are vertical. Stick one 2-inch wide piece to the bottom of the vertical piece so it lies at right angles to the vertical piece. Stick the other 2-inch piece to the top of the vertical piece. Stick one of the 6-inch-wide pieces to the opposite edge at the bottom and the other 6-inch piece at the top.
Attach the other cabinet height and width piece to the glued faces of the 6- and 2-inch wide pieces, to form the basic cabinet frame. The cabinet has an open back with two 6-inch-wide support braces while the front has two 2-inch-wide support braces. Glue the top of the cabinet. Place the cabinet width and depth piece on top of the cabinet frame.
Reinforce all joints with countersunk 1-inch-long screws and a hammer drill with a screwdriver drill bit. Screw the two hinges to one cabinet height edge of the remaining hardwood piece so they are equidistant from the corners. Turn the piece over and screw the handle to the opposite edge of the piece, to form the cabinet door. Stand the door in place at the front of the cabinet. Screw the hinges to the inside of the cabinet frame.