Can hot water freeze faster than cold water? If it can, why? If it can't, why not

.....Just a challenge from school....I'd really appreciate the help! ^.^

Thats an old canard.
It MIGHT, in a refrigerator, if:
* the warmer water starts the refrigerator working so there's more cooling available,
* and the warm water sets up a persistent convection current that
moves the cold air past it faster.
Otherwise, ... No.

Yes hot water could freeze faster then cold water, put the cold water in a freezer and dip the warm water in liquid nitrogen.

PS: The glass might break in the warm cup due to a fast temp change.