How many ways can 8 people be seated in a row?

If there is a man on the first seat, there has to be a woman on the second, a man on the third so forth. Alternatively, we could start with a woman, then put a man, then a woman and so forth. In any case, if we decide which gender to put on the first seat, the genders for the others seats are forced upon us. So there are only two ways in which we can divide the eight aligned seats into "man-seats" and "woman-seats" without violating the rule that no two men and no two women may sit next to each other.

Once you have chosen where to seat the men and where the women you can permute the two groups arbitrarily, giving $4!$ possibilities each. So in total the number of possible constellations is $$ 2\cdot 4!\cdot 4!=1152. $$