Students are prohibited (1)/ to bring cycles (2)/ into the college. (3)/ No error.(4)

Answer

2

Explanation

from bringing will replace to bring because -bringing cycles is the Object after a Preposition, and
from (Prep.) will be used because it indicates prevention/prohibition/restraint
Look at the examples given below:
He was saved `underset(Prep.)underset(darr)("from")underset("-ing Verb")underset(darr)("choking")` to death.
Nothing prevents him `underset(Prep.)underset(darr)("from")underset("Gerund")underset(darr)("leaving")`
Hence, from bringing cycles is the right usage.