Referring to the mirror in the slide, create a frame with the license plates. Measure the outside dimensions of the frame and the dimensions of the center opening.
Have the mirror cut to the center opening dimensions. Cut the plywood 1/2 inch smaller all around than the outside dimensions of the frame so it won't cover the license plate holes. Paint both sides of the plywood. Let dry.
On the plywood draw diagonal lines from corner to corner, forming a large X. In each upper corner, make a mark 4 inches down from the top edge and 4 inches in from the side edge. Make a second mark in each corner 4 inches down from the top edge and 5 inches in from the side edge. Drill a hole for hanging at each mark. Thread the wire through one set of holes and twist it on itself to secure. Repeat with the other end of the wire and the other set of holes to create a wire hanger.
Place the mirror in the center of the plywood, aligning the corners with the X. Draw around the mirror, then set it aside.
Apply mirror mastic within the drawn lines and press the mirror into place. Apply mirror mastic to the remaining exposed plywood and put the license plates in place. Place heavy books or other items on the frame and let it dry for 24 to 48 hours.