1. Tell me the reason why you came late.

Question

2. Tell me why you came late.
(In #1, 'why' is a relative adverb. In #2, 'why' is a relative adverb or an interrogative adverb. Is that right?)

3. This is how he solved the problem.
(In this sentence, 'how' is a relative adverb. 'the way' is deleted before 'how.' Is that right?)

Answer 1

Both "why" and "how" are interrogative adverbs.

#1 is awkward and wordy (delete "the reason" or delete "why"; #2 and #3 are fine. And yes, "the way" should not occur before "how."