Hamlet resolves to kill king claudius, but then he does not take advantage of an opportunity to do so. how does this show that hamlet is a round character? he represents the concept of failure. he acts in contradictory ways. he has forgiven claudius. he teaches the audience a moral lesson.

He cares nothing at all about the audience and their moral state.
Forgiven Claudius? Not on your life. Revenge is still uppermost in his mind.
He did not fail. He had an excellent reason for not killing Claudius.

You know that it is not the second answer really either. Since the others are wrong, all you can pick is that second answer.

The actual answer is that if he kills Claudius where and when he has the chance, Claudius according to Catholic belief will be in a state of grace and all sins will be forgiven. That's the last thing that Hamlet wants.

Second choice Hamlet acts in Contradictory ways <<<< answer.

You may get it wrong. If you do you should argue that there really isn't an answer. But let it go if your marker insists. Don't make enemies of people who have power over you.