I have the thermostat in an apartment I have no access to and I want to move it to my apartment.

I took a few pictures of the furnace and other wiring I found.

Coming from the furnace there are two whites cables, that going into a box. Inside the box the two whites cables are connected to a white and a red cable, see the first picture.

From there they run in a brown encasing, to the wall where the blue wire is connected to a screw cap ( this wire is not connected to anything in the 1st pic)
The red wire is cut, it was connected to a white wire in the 1st pic.
The other white wire is connected to a screw cap and goes to a white wire.
Another white wire from the transformer and a green wire.
The red wire from the transformer goes to a red wire with a screw cap.

So I see that there probably are four wires that appear to be going to a thermostat; blue, white, green and red.

I think I got it figured out. What do you think?

I can't read the labels on any of the terminals in your photos. Nor can I tell where any of the wires are going. I will paste in a general explanation of how thermostats are usually wired up. You need a cable going from the thermostat to the furnace with the wires connected to the same terminals at each end. The only other wires you need are inside the furnace, and a pair going out to the coil of any A/C compressor relay. Let me know if you need more help

Usually there is a 24 volt AC transformer in the furnace with the secondary winding connected to a red wire running to the thermostat and a blue wire, common, to the gas valve, A/C relay, and fan relay. From the thermostat there will be white wire to the gas valve, yellow to the A/C, and green to the fan. The thermostat is wired to switch the power from the red to the white, yellow, and green as needed with the blue completing the circuit. Most thermostats and furnaces have the contacts labeled R, B or C, W, Y, and G for the corresponding wire colors. It may be wired to have the A/C control wires return to the furnace and its controls and then a second wire goes to the A/C unit. Internal wiring may replace the green wire if the thermostat does not give you the option of fan only or continuous fan. Digital or programmable thermostats may need the blue wire connected to them.