I want to know why are you late.
Heard that sentence before and wondered why it doesn’t sound quite right?
Why are you late?
is a grammatically correct sentence.
The question word why is followed by the verb (are) and then the subject (you). The sentence ends with a question mark because it is a question.
However, when a question word comes in the middle of a sentence, the word order changes. This makes it an embedded question so the word order changes.
I want to know why you are late.
The question word why is followed by the subject and then the verb (like in any other statement).
She wants to know where you have kept the iron.
Mary doesn’t know when the meeting is.
I don’t know what you mean by that.
The visitor wants to know how the system functions.