Cut one 2-by-4 into 3 equal 4-foot pieces. Cut the other in to 2 equal 6-foot pieces. Cut the 2-by-12 into 4 equal 4-foot pieces.
Lay out two sections of four foot 2-by-4s, roughly 3 feet apart and parallel, on a level working surface. Place one section of 2-by-12 across the parallel 2-by-4s and hammer it into place, with two nails on either end of the 2-by-12, on both sides, into the 2-by-12 and through to the 2-by-4. Repeat this for the three remaining sections of 2-by-12 so that you have built a wall of 2-by-12s, backed by the 2-by-4s.
Screw the hinge into place on the top of the top 2-by-12, just to the outside the 2-by-4 backing. The pivot point of the hinge should hang over the back of the wall, which is the side with the 2-by-4s on it, while the two ends of the hinge should both point forward. Screw the other hinge into place on the other side of the wall with the same orientation.
Place the end of one of the 6-foot sections of 2-by-4 on to the other side of the hinge and screw it into place there. The 6-foot sections of 2-by-4 will act as the bracing legs of the rebounder wall, so they should point back, away from the front of the wall. You can screw the hinge onto the cut end of the 2-by-4, though screwing it into the face of the 2-by-4, just down from the end, will work equally well, and there will be less chance of the wood splitting with this approach. Repeat this for the other side with the other section of 6-foot 2-by-4.
Nail the remaining 4-foot section of 2-by-4 across the bottom of the legs of the rebounder wall to add strength to them.