My uncle Robert told us about the time when he backpacked across the island of Luzon.
Answer:
a. adjective
Step-by-step explanation:
The italicized clause describes or modifies the noun "time". Adverb clauses do not modify nouns, but adjective clause do.
The clause "when he backpacked across the island of Luzon" is an adjective clause. It is describing a noun and, therefore, acting as an adjective in the sentence.