It's so grammatically so hard for native speaker. 1.안나가 알레크스를 좋아하는 줄 알아요" Actually no.1 is worng sentence. 은/는 줄 알다/모르다 only can use with past tense. I don't know how can i explain that. But It's kind of feeling. 은/는 줄 알다/ 모르다 means, For example, I like A. But you think I like B. Someday we talk about that. I say 'I like A'. You say, 'Reall? I thought you like B!!' In this situation, We can use 은/는 줄 알다/ 모르다. I say, 나는 A를 좋아해요. You say, 정말요? 저는 당신이 B를 좋아하는 줄 알았어요! Can you understand that? You 'knew' wrong information. But no.2 always can use. 은/는 것 알다/모르다. For example, In above situation I like A, You knew I like A. I say, I like A. You say, I know that. I say, 저는 A를 좋아해요. You say, 저는 당신이 A를 좋아하는 것을 알고 있었어요. Also you can use present. Sorry, My English is so awkward. If you don't understand, Feel free to tell me. If you can understand some korean, and you have a Skype, We can talk on Skype.

This is a tricky one to answer, but I'll have a try: 1. 은/는 줄 알다 means "to mistakenly think that..." - 제가 철수 좋아하는 줄 알아요. He(or she) mistakenly thinks that I like Cholsu. - 제가 밥한 줄 알아요. He(or she) mistakenly thinks that it's I who cooked rice. (I don't think the first-person singular "I" could be the subject in this case.) (in the past tense) - 너도 같이 가는 줄 알았어. I thought you were going to come with us(but you weren't) - 집에 간 줄 알았어. I thought you went home(but you didn't) 2. 은/는 줄 모르다 means "to not know that......", I think this one is a bit confusing because something is missing in it, like 은 and 도. 내가 좋아하는 줄은 몰라. He(or she) doesn't know I like him(or her). 너도 같이 가는 줄은 몰라. He(or she) doesn't know you are going to come with us. 걔는 내가 여기 있는 줄도 몰라! He(or she) doesn't know even that I'm here! 은/는 거 알다(or 모르다) means "to (not) know that......" and that's about it. 1. 안나가 알렉스를 좋아하는 줄 알아요. He(or she) mistakenly thinks that Anna likes Alex. 2. 안나가 알렉스를 좋아하는 걸 알아요. I know that Anna likes Alex. (We say 거 more often, in everyday conversation.) 내 생일인 줄 알고 있었어? means either "Did you know it was my birthday?" or "Did you think it was my birthday?". "내 생일인 거 알고 있었어?" means only "Did you know it was my birthday?".

* ~ㄴ 걸 알다 = ~ ㄴ 것을 알다 = know that ~. * ~ㄴ 줄(로) 알다 = ~ㄴ 걸로 알다 = ~ ㄴ 것으로 알다 = ~ㄴ 것이라고 알다 = understand that ~. ex) 내 생일인 줄로 알았어? = 내 생일인 걸로 알았어? = 내 생일인 것으로 알았어? = Did you understand that it was my birthday? (=It was not my birthday.) * ~ㄴ 줄 알다 = ~ㄴ 걸 알다 = ~ ㄴ지 알다 = ~ㄴ 것인지 알다 = know if ~. ex) 내 생일인 줄 알았어? = 내 생일인 걸 알았어? = 내 생일인지 알았어? = Did you know if it was my birthday? (=I am wondering if you knew it.) * Notice that sometimes "~ㄴ 줄 알았어?" could sound like "Did you understand that ~?".

Have you listened this lesson? Read the PDF as well. http://www.talktomeinkorean.com/lessons/l6l26/