This answer is not correct. Hyperconjugation resonance is the momentary donation of electrons from adjacent carbon-hydrogen bonds to electron deficient sites. The protonated amine as well as the protonated alcohol may have positive charges but the only orbitals available are in the 3rd energy level, they both have full octets.
The methyl group is an electron donating group by induction but both molecules are the same with respect to this effect. Think how these compounds differ and try another answer.