White wires are hot, black nueteral on one motor, red wires hot, blue wires ground/nueteral on the other 3. You need a seperate momentary contact button switch for each movement. 4 motors that reverse directions, so 8 total. That's all I saw. No reversing slider switch. Marklin control boxes work this way too.
Imagine a line drawn along the bottom row of contacts inside the box connecting them all. Then a switch between each of them them and the output terminal contacts along the top row of the box contacts. A switch schenmatic is a line with a break in it on an angle.
The nueteral ground can be common to the box/switches to the 3 motors. I would seperate the gantry forward/reverse motor from these, as it has black and white wires.
I looked at one for auction on Catawiki.
Test your connections and operations before soldering up.

Ok, I looked at the traveling gantry crane. The same wiring principle applies as in basic current flow. If the wires are green, or yellow, or brown, just keep colors together to avoid a short circuit. Polarity can be remedied after testing if the motors don't sync in the same directions if need be. Just reverse the opposite contact connections from the motors.