What is the word that means something cannot be done under any circumstances?

There isn't one single perfect word that means something cannot be done under any circumstances. However, depending on the context, you could use:

Formal:

* Impossible: This is the most common and direct option.

* Impractical: This suggests that while it's not impossible, it's highly unlikely or unreasonable.

* Unfeasible: Similar to impractical, but implies more significant difficulties.

* Prohibited: This suggests a rule or law preventing the action.

Informal:

* Out of the question: This is a conversational way to say something is not possible.

* No way: This is a strong and definitive statement of impossibility.

* Forget about it: This implies the action is completely off the table.

The best word to use will depend on the specific situation and the level of formality you need.