The number of ways the 9 people can line up without restriction as to whether the
tallest woman is in line ahead of or behind the tallest man, is 9! ways.  But in
exactly half of those 9! ways, the tallest woman was ahead of the tallest man,
and in exactly half of those 9! ways, the tallest woman was behind the tallest man.

So the answer is  = 181440 ways.

Edwin