Distributing gloves to six sisters

Given $6$ distinct pairs of gloves, $12$ distinct gloves in all, how many ways are there to distribute $2$ gloves to each of $6$ sisters, regardless of whether they receive a wearable pair of a right handed glove and a left handed glove.

I'm having trouble with this problem. Can someone give me some hints on how to approach it?

It's $\frac{12!}{(2!)^6}$, consider all possible permutations of the gloves, and then give the first two to the first sister, the next two to the second and so on.