This is a combinations question. We're asked how many subgroups of 2 can we make out of 12 objects.

The combinations formula is important to know for the GMAT, especially if you're aiming for a 600+ score.

nCk = n!/k!(n-k)!

n = total # of objects
k = number we're choosing
! = factorial

The factorial operation involves multiplying a positive integer by all the smaller positive integers. For example:

4! = 4*3*2*1
7! = 7*6*5*4*3*2*1

A couple of things to note:

0! = 1
1! = 1

Back to your question:

n=12
k=2

So:

12C2 = 12!/2!(12-2)! = 12!/2!10!

Now, we could write the whole thing out and cancel, or we could recognize that 12! = 12*11*10!, and rewrite the expression as:

12*11*10!/2*1*10! = 12*11/2 = 6*11 = 66: choose (d)

Thanks Stu!