Can you react to win condition of Gutter Palace? If not, why?

Yes, you can react to the Gutter Palace trigger — but your reaction cannot stop the win from happening.

Here's how it works:

1. At the start of your Beginning Phase, the game checks: do you have exactly 4 cards in hand and exactly 4 units at battlefields? If yes, the win condition trigger is placed on the Chain (Rule 383.3).
2. This creates a Closed State, allowing players to play Reaction cards/abilities.
3. However, per Rule 383.3.e, the "if you have exactly 4 cards in hand and exactly 4 units at battlefields" is a conditional statement that's only checked when the trigger is placed on the Chain. Once it's there, the win is locked in.
4. So if an opponent uses Gust to remove a unit in response, the win still happens — the condition isn't rechecked at resolution (FAQ #11528).

In short: you can react to the trigger itself (e.g., Gust a unit, play a reaction spell), but that won't prevent Gutter Palace from winning. The only way to stop it is to change the board/hand state before the Beginning Phase trigger checks the condition.