Conflicts belong to every workplace, and each of us experiences them. Even Jesus had some conflicts with his disciples and with the pharisees :).
Ideal candidate for a position in HR, however, should be able to solve their own conflicts, as well as conflicts between other people sharing the workplace with them.
You should emphasize in your answer that you try to avoid conflicts. Elaborate on it saying that you are honest in your communication, and always try to understand the point of view of other party.
Talk about the past
This is a behavioral question. You shouldn’t say what you would do to solve a conflict, but rather describe a conflict situation from the past and the steps you took to resolve it. You should definitely talk about the situation which you managed to solve at the end.
There is no reason to be worried if it goes about your first job application. Try to talk about a conflict situation from the school, or from your home. Your attitude matters, not the particular situation you describe.
You should always try to present yourself as attentive to the needs and feelings of the others. Don’t be afraid to admit your own mistakes.
I try to avoid conflicts with people, being attentive to the needs and feelings of my colleagues. I had a conflict with my manager in previous job only once. He believed I was doing my job ineffectively, but did not realize that I had to wait for the work of other people, without which I couldn’t complete my own job. Firstly I apologized, to calm him down, and then I tried to explain it in simple language, giving specific reasons why I hadn’t taken care of my duties in time. I understood why the supervisor was angry. His own superior was not satisfied with the results of his job. After all we managed to come to a compromise, we solved the conflict and changed the workflow between us. Everything went smoothly afterwards.