안 들어요 do not 못 들어요 cannot (passive and permanent nuance) 들 수 없어요 cannot (active and temporally nuance) There are two types of negation for a verb in Korean. 1. 안 + verb : do not (verb) 2. 못 + verb : cannot (verb) For example, 나는 복숭아를 안 먹는다. I don't eat peach.(I don't want to eat peach. ) - for the will of subject - ACTIVE 나는 복숭아를 못 먹는다. I cannot eat peach.(I want to eat peach, but I am unable eat peach for several reasons) - for situation - PASSIVE Each from has long form 1. 안 + verb = verb + 지 않다 2. 못 + verb = verb + 지 못하다 For example, 나는 복숭아를 안 먹는다. = 나는 복숭아를 먹지 않는다. 나는 복숭아를 못 먹는다. = 나는 복숭아를 먹지 못한다. ~ㄹ 수 없다 has active and temporal nuance. ~지 못하다 has passive and permanent nuance Both can be used interchangeably in many cases. Here are the differences. I cannot swim because I'm tired now.(temporally) 지금 피곤해서 수영을 할 수 없어요. (more natural) 지금 피곤해서 수영을 하지 못해요. I cannot swim because I didn't learn swimming.(as usual) 수영을 배우지 않아서 수영을 하지 못해요. (more natural) 수영을 배우지 않아서 수영을 할 수 없어요. Although I want to eat more, I cannot eat it because I ate my fill. (with the intention) 먹고 싶지만 배가 불러서 이 사과는 먹을 수 없어요. (more natural) 먹고 싶지만 배가 불러서 이 사과는 먹지 못해요.

안 들어요 means you do not want to hear. 못 들어요 and 들을 수 없어요 both mean you want to hear, but can't. 못 들어요 and 들을 수 없어요 have the same meaning, but 못 들어요 is more natural. Make sure you conjugate and spell the verbs right! 들을 수 없어요 instead of 들 수 없어요 and 못 들어요.

The first one means, "didn't hear", the second one is, "couldn't hear", and the last one is pretty close to the second one, but I believe it would be more close to, "there's no way (she/he/I, whatever) could hear". So in terms of the degree of being unable to hear, it would be in that ascending order.