Hello,
Im currently working on a Stewart platform with a touch screen. However I havent secured the wire coming from the screen correctly and one path has broken. Im not sure exactly what should I do with it. Is a soldering a good idea ?

 

Welcome to AAC!

Tape the back of the ribbon cable to prevent further damage.
If you attempt to solder the connection you are likely going to melt the plastic.

I would attempt to use #30AWG wire wrap wire to repair the broken connection. I would solder one end of the wire at the black connector.
For connecting the other end I would have to look for a suitable connection point (not on the cable) to make the repair.