Slide a stud finder along the wall in the location you selected for the desk. Mark the location of each wall stud with a pencil.
Hold 2-by-2-by-84-inch board horizontally against the wall in the selected location for the desk. Measure up to the top edge of the board and adjust its height so that is equal to the height of the metal filing cabinets. Drive a wood screw through the board into the wall at each stud marking with a screw gun to secure it to the wall. This is the wall mount board.
Position one melamine panel over the top of the wall mount board at one end. Drive wood screws through the bottom of the wall mount board into the bottom of the melamine panel every 4 to 6 inches with a screw gun. Place the second melamine board on the unused 24 inches of the wall mount board so that it is perpendicular to the wall to create the L-shaped desk. The length of the panel should extend from the wall to form the L-shape. Drive screws every 4 inches through the bottom of the wall mount board into the bottom of the second melamine panel to secure it in place.
Slide a filing cabinet under the ends of the L-shaped desk surface. The wall mounted end filing cabinet should face out from the wall. The open-ended filing cabinet on the L-extension should face in toward the inside edge of the desk for ease of access.
Place a metal L-brace on the inside edge underneath the melamine panels where they join and form a 90-degree angle. Center the brace between the joint. Drive the screws included with the brace through the mounting holes into the bottom of the melamine panels with a screw gun.