We have 6 people, 3 men, and 3 women.

On how many ways, can we sat them at aroundtable, on 6 chairs, but they must sit in this order: man, woman,man,woman... So the neighbour must be the opposite sex.

Is this correct?

$\displaystyle \frac{3!*3!}{6}$

the six in the denominator is because it's aroundtable, and we can rotate them for one place, and would be the same so it's 6 for six places.