Explanation:

- Option 1: Between

"Between" is used to indicate a location or relationship that involves two or more things. It doesn't fit this context of describing proximity.

- Option 2: With

"With" generally implies being accompanied by someone or something. It doesn't suit the context as it indicates close association rather than proximity in distance.

- Option 3: Within

"Within" suggests being inside certain boundaries or limits. In this case, it describes the proximity between Peter and Paul's homes effectively.

- Option 4: For

"For" is used to indicate purpose or duration. This doesn't apply to the context of describing distance.