HELP! Can this problem be solved with Plugging in Numbers?

It would be a pretty awkward problem to solve by plugging in numbers - I think if you were adept enough at math to see how to do that quickly, you'd likely find the actual algebra even quicker. You'd first need to find values of c and d that work in the equation given (for example, c = 2 and d = 3), then plug your value of c into each answer choice until you find one which is equal to d. If you find more than one answer that is equal to d, you'd need to pick a new set of numbers to differentiate between the remaining choices (if you try c = 2 and d = 3, you'll find that both answers C and E give you the correct value for d - that's just coincidence, so you need to try a different set of numbers to see which answer choice *always* gives the right value for d). I don't find that fast to do.

Algebraically, it's a four step problem. First cross multiply:

3c + 2d = 2cd

Then get terms with d in them to one side, since we want to solve for d:

3c = 2cd - 2d

Then factor out the d:

3c = d(2c - 2)

then divide on both sides by the thing in brackets:

3c/(2c- 2) = d

That's quite a standard sequence of steps to need to carry out in GMAT algebra, and it's much, much faster than plugging in numbers here, so it's worth learning.