Have an assistant hold two 3/4-by-8-by-24-inch boards upright on their long, thin edges. Space them parallel to each other, 1.5 feet apart. Consider these two boards the top and bottom boards. Set two 3/4-by-8 by-18-inch boards, which are the side boards, between them on each end so that the four boards form a 19 1/2-by 24-inch rectangular frame.
Set 2-inch metal L-brackets inside the frame at each corner, so that there are two brackets between each of the two boards in the frame. Drill a 3/4-inch wood screw through each of the bracket holes to attach the brackets.
Set a 3/4-by-19 1/2-by-24-inch plywood board on the ground. Lower the rectangular frame on top of this plywood board, which is the rear board. Position 2-inch metal L-brackets within the frame every six inches between the frame and the rear board. Attach these brackets with 3/4-inch wood screws.
Set a 18-by-22 1/2-inch sliding door frame with included doors within the front of the cabinet opening. Slide both doors to one side. Set 3/4-inch wood screws in each of the predrilled holes within this sliding door frame. Tighten the screws in place. Slide the doors to the other side and attach screws in all of the holes on that half of the frame.
Find the studs in the wall with a stud finder and mark them clearly. Hold the carpentry level on top of the cabinet and set it against the marked area. Drill through the rear board of the cabinet every six inches into each stud it overlaps. Attach the cabinet to the wall with 3-inch wood screws threaded through washers.