Answer:
(B) for many decades
Step-by-step explanation:
The adverb phrase in the sentence "That old lighthouse has warned sailors for many decades" is for many decades.
Adverb phrases modify verbs, adjectives, or other adverbs.
In this case, the adverb phrase for many decades modifies the verb has warned. It tells us how long the lighthouse has been warning sailors.
The other words in the sentence are either the subject (that old lighthouse), the verb (has warned), or the direct object (sailors).
Therefore, the answer is (B) for many decades.