Grammar
-았/었는지 알다
to know how much / whether something happened
Form
Past -았/었는지 + 알다 (“know whether / how much…”).
Function
Embeds an indirect question about a past event or its extent under 알다; an interrogative such as 얼마나 supplies what is being asked.
Why this form?
-았/었는지 모르다 — “not know whether / how much”: the same embedded question is governed by 모르다, indicating lack of knowledge.
Forms not to confuse
-았/었는지 모르다
언제 왔는지 몰라요. — I don’t know when he arrived.
Examples
내가 너 때문에 얼마나 참았는지 알아?! — Do you know how much I have endured because of you?!
내가 얼마나 기다렸는지 알아? — Do you know how long I waited?