Confusing, can a motor on a moving disc stop the disc? I've been troubled trying to solve this problem. 
If a motor is fixed on a moving rotating disc and the motor's rotor has another disc attached to it. What would happen if we attached the motor's disc to the the disc its on and powered the motor's to rotate the disc opposite to the disc that the motor is moving on? 
What would be the result, I couldn't figure it out. Would the system stop? If the torque of the disc= torque of the motor's disc.
EDIT: The motor is placed vertical on the disc, and the motor's attached disc(on the rotor) has the same diameter is the one it's placed on. 
 A: If the motor is fixed on a moving rotating disc there can only be one result. If you attach the rotor from the engine to the platform, then either the rotor or the platform (or the engine) will tear itself apart.
It doesn't matter if that platform is moving or not.
See my drawing; if I glued the rotor disc to the platform, it cannot rotate. If it is forced to rotate anyways, something will break. I might have misunderstood your question, so please let me know if that's the case.
Edit
After your edit of the question my drawing needs a small change, but the same principle still holds. The reason is the effect of Newton's 3rd law!
Any force applied causes an equal and opposite force. So the engine apply a force (a torque) one way will itself be forced the other way around. Since the engine is fixed to the bottom disc, this force is transfered on to this disc.
So the bottom disc experiences both forces, which are equal and opposite in direction - and so there is no net force and no change of it's motion.
The only result from this will be that the fixed parts eventually get unfixed by being damaged, scewed, twisted and broken. If the discs are very strong, this may happen within the engine, permanently damaging gears etc.

A: Yes you can use the motor to slow and stop the disk, but you have to have (1) Alignment of the motor and its load angular momentum with the disk's angular momentum, and (2) enough motor load (moment of inertia) and motor speed to fully transfer the disk's angular momentum into the motor and load.
The process of momentum transfer is done all the time on spacecraft using reaction wheels or control moment gyros. Typically an initially spin-stabilized satellite is de-spinned to a slower rotation rate, and then the reaction wheels take over to slow the spin to a stop.
Typically 3 reactions wheels or more, aligned on different axes are used so that spin rates can be controlled in all possible axes.
Over time the reaction wheels are used to keep the attitude of the satellite stable and pointing in some particular direction - against disturbances such as planetary magnetic perturbations, upper atmosphere wind disturbance if the satellite is in low earth orbit, and solar wind pressures. So the wheels over time build up angular momentum. Before the wheels 'saturate' at their maximum speed, the satellite will 'dump' momentum by despinning the wheels against propulsion system applied torque.
