-(으)ㄴ지 turns a statement into an embedded question and 모르다 says the answer is unknown. Two things happen in these lines. One is realising you were wrong about a fact: 형이 이렇게 말이 많은지 몰랐어요 'I had no idea you were this talkative'. The other is genuine puzzlement about a reason: 왜 그렇게 좋은지 모르겠는데 그냥 좋아요 'I don't know why I like it so much, I just do'. Watch for the set emphatic 얼마나 …-(으)ㄴ지 모르다, which means 'you have no idea how hot it gets' rather than actual ignorance.