Concept:The phrase "but for" means "except for" or "if not for", and it introduces the reason that stopped an action.Explanation:The sentence says: "I would have visited you but for my father's ill health."This means the planned visit did not happen.The cause of not visiting was the father's illness.So, the father's ill health stopped the speaker from visiting.Answer:The correct interpretation is: B. father's ill health prevented me from visiting you.