The ship . . . . . , Robinson arrived on the Island.

Answer: Option B

The ship having been broken, Robinson arrived on the Island.

In this sentence, the use of the participle phrase "having been broken" correctly describes an action that was completed before the main action (Robinson arriving on the island). It indicates that the ship had already been broken before Robinson arrived.

Option A: had been broken is incorrect because it requires a different sentence structure, like "The ship had been broken when Robinson arrived on the island."

Option C: having broken is incorrect because it suggests that the ship itself broke something, which is not the intended meaning.

Option D: has broken is incorrect because it indicates a present perfect tense, which doesn't fit the sequence of events where the ship breaking happened before Robinson's arrival.

Conclusion: The correct answer is Option B: having been broken, as it properly conveys the sequence of events where the ship had already been broken before Robinson arrived.