Since there are two members, and only one can go from each team, we are choosing two teams out of three. For each of those teams, we are choosing one member out of two. And since each of these choices is independent, the number of choices multiplies. So, our answer = 3C2 × 2C1 × 2C1 = 12.
The correct answer is C.
Try a little probability to sharpen your mind before the new year.