Explanation:
> "Could I ring him up? I'd rather you ____."

The phrase "I'd rather you" is followed by a past tense verb to express preference about a hypothetical or desired action, even though it's about a present or future event. This is a common structure in English when using "would rather."

Now, let's analyze the options:

- A. visit him — This is in the base form of the verb, but after "I'd rather you," we need a past tense verb. Incorrect.
- B. visited him — This is the correct form. After "I'd rather you," we use the past tense of the verb, even if referring to the present or future. Correct.
- C. would visit him — "Would" is unnecessary here because "I'd rather you" already implies a preference. Incorrect.
- D. visiting him — The gerund form ("visiting") is not appropriate after "I'd rather you." Incorrect.
- E. will visit him — The future tense "will" is not used in this structure. Incorrect.