You are creating a transverse wave in a rope by shaking your hand from side to side. Without changing the distance that your hand moves, you begin to shake it slower and slower. What happens to the frequency?

it decreases

correct.

The frequency of a wave is determined by the number of complete oscillations or cycles it completes in a given time. In this case, as you shake your hand slower and slower while maintaining the same distance, the number of oscillations or cycles that occur in a given time decreases. Therefore, the frequency of the wave decreases.