Do you write did not know or did not knew?

Answer 1

You say did not know.

I did not know the answer to his question.

This sentence is a past simple sentence. The word 'did' (past form of 'do') tells us the sentence is past. The main verb 'know' is a present form this is how you make a negative past simple sentence using 'did'. Another example:

They did not eat their lunch. (Main verb is present, 'did' is past form of 'do'.)

I do not know the answer to your question.

This is a present simple negative sentence. The word 'did' is present. The main verb 'know' is present form.

Answer 2

The correct phrase is "did not know." "Knew" is the past tense of "know," while "did not know" is the correct negative form in the past tense.