The correct option to complete the sentence "Could I ring him up? I'd rather you ...." is B. visited him. Let's break down why this is the correct choice and analyze the other options. Step-by-Step Explanation

1. Understanding the Context: The phrase "I'd rather you..." indicates a preference or desire regarding someone else's actions. In English, when expressing a preference about someone else's actions in the present or future, we typically use the subjunctive mood.
2. Subjunctive Mood: The subjunctive mood is used to express wishes, demands, or suggestions. In this case, "I'd rather you..." is a way of saying "I would prefer it if you..." followed by a verb in the past tense form. This is a common structure in English.
3. Analyzing the Options:
4. A. visit him: This option is in the base form of the verb "visit." While it sounds correct, it does not fit the grammatical structure required after "I'd rather you...". It would be more appropriate in a different context, such as "I would like you to visit him."
5. B. visited him: This is the correct option. It uses the past tense form "visited," which is appropriate after "I'd rather you..." to express a preference. It implies that the speaker prefers the action of visiting to be done by the listener.
6. C. would visit him: This option uses "would," which is not suitable in this context. "I'd rather you would visit him" is grammatically incorrect because "would" is not needed after "I'd rather you." The subjunctive form is sufficient.
7. D. visiting him: This option uses the gerund form "visiting," which does not fit the structure of the sentence. It would not convey the intended meaning of preference and is grammatically incorrect in this context.

Summary of Why B is Correct and Others are Wrong

• Correct Option (B): "visited him" is the correct choice because it follows the subjunctive mood structure after "I'd rather you...".
• Option A: "visit him" is in the base form and does not fit the required grammatical structure.
• Option C: "would visit him" incorrectly uses "would," which is unnecessary in this context.
• Option D: "visiting him" is a gerund and does not convey the intended meaning of preference.

Revision Summary

• The correct answer is B. visited him.
• Use the past tense form after "I'd rather you..." to express preferences.
• The subjunctive mood is key in expressing wishes or preferences about others' actions.
• Avoid using base forms or gerunds in this context, as they do not fit grammatically.