I don’t know the city . . . . . he lives.

The correct answer is B: where.

First, let's define the terms.

Where: An interrogative adverb used to ask about a place or location.
What: An interrogative pronoun used to ask about things or which thing.
When: An interrogative adverb used to ask about time.
Which: An interrogative pronoun used to ask about a choice from a defined set of options.

The sentence "I don’t know the city . . . . . he lives" requires an interrogative word to specify the location where the person lives. Therefore, only "where" fits grammatically and contextually.

The sentence should read: "I don’t know the city where he lives." The clause "where he lives" acts as a relative clause modifying "city", specifying which city is being discussed.

Options A, C, and D are incorrect because they don't address the question of location. "What" asks about the identity of a thing, "when" asks about time, and "which" asks about a selection from a set of possibilities. None of these are relevant to the location of the city.