Answer:
1. "who lives next door" - this is an adverbial clause modifying the noun "man".
2. "who delivered the triplets" - this is an adverbial clause modifying the noun "woman".
3. "that I read" - this is an adverbial clause modifying the noun "novel".
4. "that picked the students" - this is an adverbial clause modifying the noun "bus".
5. "who was robbed in the last hour" - this is an adverbial clause modifying the noun "boxer".
6. "which he bought in South Africa" - this is an adverbial clause modifying the noun "watch".
Adverbial clauses are clauses that modify a verb, an adjective, or an adverb, and often answer the questions of how, when, where, why, or to what extent.