In the above mechanism it is required to find the generalized coordinates to write equation of motion of the MDOF system. I just want to ask how do we actually approach such a problem? How to identify which kinematic degrees of freedom are relevant and independent?

The answer given in this particular case is 4. Two rotation of the pulleys, and two vertical motions of the masses B and C. Now how to visualize this? How do I methodically come to this conclusion? Again, is there any other combination possible?

All pulleys are massless and frictionless.