Explanation:
an octagon has 8 sides.
in a regular octagon all 8 sides are equally long.
the perimeter is therefore
8 × side length = 120 ft.
in fact, that tells us that the individual side length is
side length = 120/8 = 15 ft
now the new perimeter is
8 × side length new = 168 ft
side length new = 168/8 = 21 ft
so, we see that the individual side lengths increased from 15 to 21 ft and therefore by 21 - 15 = 6 ft.