Distressed wood floating shelves are an aerodynamic, minimalist style of shelving and are often used in modern interior design. The beauty of these shelves is that there are no visible signs of the way the shelves are fixed to the wall. It creates the illusion that they are simply floating. Furthermore, the trick to free-floating shelves is very simple. The shelves are hollow boxes and the backs sit on a fixing system or support. That is attached to the wall.
Cut the wood 2 by 2 on two sides of the 12-inch platform and on a 43-inch wall stud. Moreover, cut the plywood into a 12-by-48-inch top and bottom panel and a 3 1/2 by the 48-inch front panel. Place the side shelves 2 by 2 inches apart by 48 and place a 48-inch plywood panel over them. Place the front panel on one of the open ends of the platform so that it is flush with the sides, up and down. Secure in place with headless nails.
Find three studs of the wall on the wall where you want to hang the floating platform. Mark the position of the studs and draw a level line between them for the position of the cleats. Attach the fixing system to the wall. Slot the open end of the shelf box over the fixing system. There will be about 1/2 inch of space on each side, but it will be a perfect fit along the length of the platform.