Step 1: Space saving/hiding part 1
So the six red boxes on the top in a 3 by 2 grid are the things that you want to put away. The black strips and the blue spheres inside of them are conveyor belts. They move the boxes labeled A through F (the things you want to store) to hydraulic pumps, which move it down so you can use it.
On the third image, it labels the conveyor belts and the storage. Here is the path from storage to room:
Box A: To Conveyor belt 1, to 2, to 3, to 6 (hydraulic pump)
Box C: to C.B. 3 to 6
Box E: To C.B. 5, to 4, to 3, to 6
Box B: From C.B. 7, to 8, to 9, to 12 (hydraulic pump)
Box D: To C.B. 9 to 12
Box F: To C.B. 11, to 10, to 9, to 12
There is a ceiling under the conveyor belts, holding up the whole thing.