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Step-by-step build — 4 steps. Also available as a print sheet.
Pre-drill — pocket holes or countersunk pilots, your choice — and join the top and bottom to the back, outside edges flush, glue at both joints. That's the C; it's floppy on purpose right now.
Measure and mark the brace's position at the top, middle, and bottom (per the diagram), stand the 1x6 vertically against the back, and screw through pre-drilled holes with glue.
This board is the table's spine — the cantilevered top pushes down, the brace pushes back. Full screws, full glue, no shortcuts on the boring part.
Attach the 1x2 side footers to the bottom, then the end footers to the bottom and side footers. The back footer end can't take a direct screw — the source says don't worry, and don't: this trim carries nothing. Glue and whatever fastener reaches.
Screw the four 1-1/2" casters to the bottom corners, then confirm the whole bottom assembly still clears your sofa's under-height — that clearance is the entire product.
Fill every countersink, sand to 120, prime and paint. Roll it over the sofa foot, open the laptop, and accept that dinner now happens here too.