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Step-by-step build — 6 steps. Also available as a print sheet.
Build the two side leg frames with the jig set for 3/4" stock and 1-1/4" pocket screws. Make them match.
Build the back leg frame to the given dimensions. The angled piece is the 12-1/2" 1x2 with 45° cuts — it braces the folding geometry. Pocket holes set for 3/4" stock, 1-1/4" screws.
Note the corrected length — the shelf frame 1x4s are 37-1/8", cut to fit, not the printed diagram number. Inset your 1x2s 3/4" from the ends of the 1x4s and attach with 1-1/4" screws and glue, two screws per shelf per side.
Evenly space the remaining shelf boards, gluing and screwing each in place with two screws per board per side.
You can pocket-hole the top boards together, but planking them on a scrap board with a slight gap between boards is better for an outdoor piece — the gap drains water and lets the boards move. Arrange them inside the 1x6 frame.
Before screwing hinges on, stand the sides to be hinged next to each other and test-fold with the hinge in hand to confirm the correct orientation, then scribe the screw locations. Mount the hinges, sand, and apply an exterior finish. Now it folds flat for storage.