Mark a square on the 4' x 4' piece of plywood. The square should be 3' across and 2' high, starting about 6" down from the top of the plywood piece. Use the jigsaw to cut the square out. Discard the square.
Lay the 4' x 4' plywood piece face down and place the 4' x 2' pieces on either side of it, also face down. Place two piano hinges between each side piece and the middle piece, six inches from top and bottom edges. Use the pencil to mark where you'll need to drill holes for the hinges, then remove the hinges.
Drill holes for the hinges and attach them so that the two side pieces can now swing in and out from the center. Stand the unit up and install the coat hangers on the inside upper right and left corners of the center piece.
Cut the curtain fabric into two pieces 4' high and 2' across. Lay the wooden dowel across both pieces and fold the edge of the curtain fabric down over the dowel. Sew both pieces in place or use fabric glue, allowing enough room around the dowel for the curtains to slide back and forth. Hem the edges of the curtain pieces or apply fabric glue to keep them from fraying.
Set the dowel and curtains into place on the coat hooks.
Paint the outside of the puppet theater. You could also sew colorful patches onto the "outside" showing through the stage side of the curtains.