The species that act as acid are the ones that donates H⁺ in the reaction.
Since we are working with an equilibrium, we have to consider both directions.
From left to right, we have H₂O turning into OH⁻ because it lost one H⁺, so H₂O is acting as an acid in the forward reaction.
From right to left, we have CH₃NH₃⁺ tunrning into CH₃NH₂ because it lost one H⁺, so CH₃NH₃⁺ is acting as an acid in the backwards reaction.
So, the species that act as acids are H₂O and CH₃NH₃⁺, I and II only.