Determine which of the provided alternative words cannot be formed using the letters of the given word PUNISHMENT.

Let's check the letters of each option against the pool available in PUNISHMENT $\text{{P, U, N, I, S, H, M, E, N, T}}$:
* PUSH: $\text{{P, U, S, H}}$ are all present.
* PENT: $\text{{P, E, N, T}}$ are all present.
* PAIN: Requires the letter 'A', which is not present anywhere in the word "PUNISHMENT".
* SENT: $\text{{S, E, N, T}}$ are all present.

Hence, the word PAIN cannot be formed.