You want to say the action is unavoidable — there is no honest way out but to do it.
序 · The move
1Find the action that has no way out, and put its verb in the final slot.Is the action forced by circumstance, not just chosen?
2Pick the middle modal: 得 for a duty/obligation, 能 for an ability that can't be withheld, 可 for a permission/caution that can't be skipped.Does the chosen modal match the kind of pressure (must-do vs can't-hold-back vs mustn't-neglect)?
3Wrap it: 不 + modal + 不 + verb.Read the two 不's — do they cancel to a forced positive, not a plain negative?
例 · Examples
1他要搬家了，所以不得不cannot-not → has no choice but to轉學transfer schools。
He's moving house, so he has no choice but to transfer schools.
必須 states the requirement flat and forward (you must do X); 不能不/不得不 reaches the same must by closing off every other door (you cannot NOT do X). Same outcome, and the double negation locates the pressure in having no alternative.
不能 / 不得 / 不可
A single 不 before the modal forbids the action (不能去 = cannot go). Adding the second 不 flips it back to compulsion (不能不去 = cannot not go = must go). One 不 = forbidden; two 不's = forced.
✗ 我不得不洗衣服了，但是我不洗。 → ✓ 我不得不洗衣服。 (the construction already commits to doing it; you cannot then refuse)
✗ 不得不去嗎？我很想去。 → ✓ 我很想去。 (不得不 marks the action as unwanted-but-forced; drop it when the action is desired)
✗ 這件事不可不能小心。 → ✓ 這件事不可不小心。 (one modal sits between the two 不's; do not stack two modals)
English "cannot not" sounds like a clumsy double negative to be avoided; in Chinese 不能不 is the idiomatic way to say "have no choice but to," and reads as natural emphasis.