Explanation:

- By hook or by crook: This idiom means achieving something by any means necessary, whether fair or unfair. It implies persistent effort to attain a goal.

- Option 1: By a narrow margin

- This means achieving something with little room to spare, or just barely.

- Option 2: By any means

- This matches the idiom perfectly. It represents attaining a goal using any available method, whether conventional or not.

- Option 3: By default

- Implies something happened because of a lack of opposition or alternative.

- Option 4: By mistake

- Means an action done unintentionally or by accident.