Let Everyone Speak
Some people use aggressive, non-stop verbal attacks to silence their opponents during a workplace conflict. Supervisors might be able to get away with that style of communication, but it won't score any points for your reputation as a tactful professional.
Merely silencing a co-worker or refusing to even consider the situation from his or her perspective rarely leads to a lasting resolution. So don't turn a basic conflict into a one-sided monologue. Take the time to listen and try to learn something from the situation.
Let the other person clarify his or her perspective and opinion on the issue. It may be helpful to apply a time limit to the discussion. Doing so helps each person speak about the issues that really matter and reduces tangential (and emotion-fueled) conversational clutter that has little bearing on the conflict.