The length of the shadow on flat ground of a man who is 6 feet tall and is standing up straight is 8 feet. the distance between the top of his head and the top of his head in the shadow is feet.

It would be 10 ft.

You set up a right triangle with the base being 8 ft (the shadow), the height being 6 ft (his height) and you need the hypotenuse, a straight line from his actual head to his head in the shadow.

a^2 + b^2 = c^2
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
take the square root of both sides
10 = c