Lay two 20-inch boards parallel with their outside edges 20 inches apart. Lay a 20-by-20-inch sheet of plywood on top of the boards so the edges are flush and screw through the plywood and into the boards. Use four 2-inch screws for each board. Repeat this step with the last two boards and the other 20-by-20-inch sheet. These are the sides to your hanging projector mount.
Position the sides to your mount upright and on edge so the boards are horizontal. Space the sides 18 inches apart and lay your 18-by-20-inch sheet of plywood on the bottom boards. Screw the plywood to the boards so the edges are flush. Use four 2-inch screws for each board.
Locate studs in the ceiling where you wish to mount your projector using your stud finder. Position top two 20-inch boards on the mount over the studs on the ceiling and screw four 5-inch screws through each board and into the studs. Place your projector on the ceiling mount facing a wall or projector screen.