I used a compound mitre saw to cut the 12 frame pieces to length. You could also use a radial arm saw or tablesaw; just fit your saw with a stop block to ensure identical pieces.
     Assemble each frame on a flat surface using glue only, and clamp. Once the glue has set, remove the clamps and plunge a biscuit slot across the back of each mitred joint. Place a glued biscuit into the slot. Joining the frame pieces this way avoids the hassle of trying to capture a biscuit in the mitre joint and lining everything up all in one operation. The protruding half of the biscuit can be sanded flush when the glue is dry.

Putting It All Together

Affix the frames to the boxes using a couple of #10 biscuits. Then attach the back which you’ve cut to size. I planed my backs to 3/8" on one side only to keep the profile of the project as narrow as possible, but you can leave the back full thickness if you don’t have a surface planer. The backs should be fastened securely using biscuits, as they bear the weight of the frame and its contents.
     Finally, seat each puck light in its opening and secure with the tiny screws provided. A sawtooth hanger centred on the top of each box back takes care of hanging each unit.
     Concealing the wires that power each light is key to the success of these box frames. Because the lights are low voltage, the wires can be snaked through walls without using junction boxes to house the connections. I pried off the baseboard below my intended hanging spot and used fish tape to get the wires from the frames to the floor. A groove milled in the back of the baseboard will allow the wires to run to the transformer—which is hidden behind a nearby cabinet—without being seen.