1. I know why she was late.
2. I wonder why she was late for school.
3. I doubt why she came back home late.
4. He told me how he got there.
5. He asked me why I didn't study.
6. He showed me how to get to the station.
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Are they all grammatical? Are both 'why' and'how' interrogative adverbs in the sentences?
All are grammatically correct, but #3 seems awkward. For that one, it'd be better to write/say, "I doubt the reason she gave for coming home late."
1. "I know why she was late." - This sentence is grammatically correct. "Why" in this sentence is an interrogative adverb, as it is used to ask for the reason or cause of someone being late.
2. "I wonder why she was late for school." - This sentence is also grammatically correct. "Why" in this sentence is again an interrogative adverb, used to inquire about the reason someone was late for school.
3. "I doubt why she came back home late." - This sentence is not grammatically correct. The verb "doubt" is typically not followed by an interrogative word like "why." A better phrasing would be "I doubt that she came back home late."
4. "He told me how he got there." - This sentence is grammatically correct. "How" in this sentence is an interrogative adverb, used to inquire about the manner or method used to get to a particular place.
5. "He asked me why I didn't study." - This sentence is grammatically correct. "Why" in this sentence is an interrogative adverb, used to inquire about the reason or motive for not studying.
6. "He showed me how to get to the station." - This sentence is grammatically correct. "How" in this sentence is an interrogative adverb, used to inquire about the manner or method of getting to the station.