Final answer:
The hiker must hike down 32 feet to return to the starting point as the distance up and down the mountain to return to the same point is equal.
Step-by-step explanation:
The question pertains to basic arithmetic and understanding of distance calculation. If a hiker climbs 32 feet up a mountain, to return to their starting point, they must hike 32 feet down the mountain. This is because the distance ascended and descended is the same in order to return to the initial elevation.