Arrange the two 46-by-25-inch sheets of pressure-treated plywood and the two 23-by-25-inch sheets in a rectangle shape. Stand all four boards upright on their 46- and 23-inch edges and sandwich the two shorter boards between the ends of the longer ones.
Have someone help you hold the frame together while you drive 2-inch wood screws through the 46-by-25-inch boards into the thickness of the smaller boards. When finished you should have a four-sided frame for your deck box.
Fit a 1 1/2-inch metal corner brace over the corner formed by the joint between two side panels. Adjust the position of the brace so it is about 6 inches up from the bottom of the storage box frame. Screw the brace into the frame, using 3/4-inch wood screws.
Install an additional brace about 6 inches down from the top of the box on the same side. Repeat this process to install two braces in all four corners of the rectangular storage box frame. These braces will reinforce the walls of the storage box.
Lay the 23-by-44 1/2-by-1-inch sheet of pressure-treated plywood inside the rectangular frame you just constructed for the bottom panel. All four sides of the bottom panel should be flush with the inside edges of the four side panels. Drive 2-inch wood screws through the side panels into the bottom panel to secure it in place.
Screw two 1 1/2-inch metal corner braces into the bottom of the storage box frame to reinforce the joints between the side panels and bottom panel. Attach the braces, using 3/4-inch wood screws. Position the braces approximately 6 inches from the corners along all four sides at the bottom of the storage box.
Lay the 47-by-25-by-1-inch sheet of pressure-treated plywood flat on top of the storage box frame for the lid. Attach two 2-inch metal hinges along the back edge of the lid, using 1-inch wood screws.
Adjust the lid so the edges align with the edges of the storage box frame. Screw the other side of each hinge into the back side of the storage box frame, using 1-inch wood screws. Raise and lower the lid to test the hinges.
Paint or stain your completed deck storage box. After the paint or stain has dried, apply one or more coats of clear varnish or polyurethane to protect the deck box from water damage.