The answer GMAT wants is 12. You fix one guy to a seat and alternate man-woman. Now, the other two guys can be arranged in only two different ways with respect to that one guy you fixed in one seat. So, that's 2! ways. The women can be arranged in 3! ways with respect to the one guy. So, it's 2!*3!.
However
If each chair itself is unique, then shouldn't the answer be 72? The question assumes that the seats themselves don't matter, and that only the relative arrangement of people matters. So, if the seats actually mattered, say, seat A is a terrible chair that's about to fall apart, seat B is an Eames lounge chair, seat C is a massage chair, seat D is closest to the window, seat E is closest to the bathroom, and seat F is next to a different loud table, then such a scenario does exist, and the answer would need to be 72.
So, calculate 12 as you did above from one fixed guy in seat A, then move the guy you fixed to seat B, then C, then D, etc. That's 72 combinations, since each seat with respect to one guy has 12 arrangements and there are six seats total (12*6). Another way to do it is to think of each seat as M1-W2-M3-W4-M5-W6 (man seat#; woman seat#) around a table and multiply the combination, so after simplyfing it's 3*3*2*2*1*1 = 36. Those are only for the odd numbered seats for men, and even numbered seats for women, so the answer needs to be double that, giving us 72.
If 12 and 72 were both answer choices, I'd pick 12 but with serious protest. GMAT may ask for unique orders of people only, so the same order but in different chairs may be disqualified in GMAT's eyes. But, the GMAT doesn't specify that they want only unique orders of people - is it somehow implied in the question? The question itself is insufficient to draw a conclusion, esp. if 12 and 72 are both answer choices. Any thoughts?