Before we move onto the assembly of the cabinet carcase, we need to do one more thing: we need to cut rabbets into the inside-back edges of the two cabinet sides to accommodate the plywood back pieces.
Set up your table saw with a stacked dado set. Insert chippers to accommodate a 3/4" wide cut, and raise the blade to a height of 3/8".
Clamp a sacrificial strip of stock to the fence of your table saw, and move the fence until it is just touching the dado blade. Then, make a pencil mark one inch in front of the leading edge of the blade.
Place the right-side piece of the cabinet inside-face down on the table, with the back edge against the fence. Cut a rabbet from the top-rear corner (on the inside face) downward until you reach the pencil mark with the bottom of the board, and turn off the saw before removing the piece. You should end up with a rabbet that extends down the back of the cabinet from the top-rear corner to about an inch above the floor.
Move the fence to the other side of the blade, and repeat the steps with the other side of the cabinet.
With the rabbets complete, it's time for some carcase assembly. Begin by attaching the two sides of the cabinet to the sides of the cabinet base using some 1 1/4" finish nails (either by hand or with a pneumatic nailer).
Next, place the bottom shelf onto the plywood base and adjust so that the front of the shelf is flush with the front of the sides and tack in place with finish nails. Add a couple of nails from the sides through into the bottom shelf for strength.
Then, attach the 12" wide rear piece into the rabbet in back and on top of the cabinet base using glue and finish nails. Also attach the top-back strut in place at the top of the rabbet using glue and finish nails.
Finally, attach the front face piece in-between the top front corners of the two sides using finish nails.