On each 32" x 14" side panel, mark a line 12-1/4" in from 14" edge. Mark out three screw holes. On the opposite side of each panel, mark a line at 12" from the same side, which will serve as a straight line to register the internal rib. I plugged the screw holes for looks, though this is not strictly necessary; if you want, counter-bore each screw hole with a 3/8" bit, a 1/4" deep.
Coat one end of the rib with a thin, even layer of wood glue. Tilt up and align one side of the 3/4" rib panel with the 12" mark on the side panel. Pre-drill and screw together, using a square to check that everything is flush. Attach the door track parallel to the rib, flush with the front of the 3/4" side.
Repeat for the matching 1/2" side panel, forming an asymmetrical "H"-shaped arrangement when viewed from above. Coat the top edges of the "H" with a thin, even layer of wood glue and lay on the top, making sure all corners are flush (tweaking the underlying structure as necessary), screw the top to the sides and ribs. Lay out your screw holes evenly for a neat appearance.
Halfway up the inside, drill out 6 3/8" diameter holes 3/8" deep—two on each side and two on the stiffening rib—and glue in 3/4" chunks of dowel to serve as shelf pins. Keep in mind as you assemble the boxes that you must make 2 sets of 2 boxes, mirroring the arrangement of the 3/4" and 1/2" sides.
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