In principle, peace comes through shared understanding, and shared understanding comes through listening. If you hear things incorrectly, or not at all, you are likely to proceed on false assumptions which are likely to give way later and cause conflict. The best way to ensure good listening is to demonstrate it.
Practical Tip: Are you listening? Prove it. After you have heard someone say something, demonstrate that you heard the person and understood what was said. Saying “I understand” is not a demonstration. (1) As you listen, show that you are paying attention with silent expressions and perhaps an encouraging word or two. (2) After hearing, reflect back what you heard. Ideally, repeat the main points, use a mix of the actual words they used and some of your own, and try to name the feelings expressed, such as: “My, that must have made you feel ________.” Let the speaker judge if you got it right. If you missed, no problem; try different words and talk it through until you “get it,” and the person agrees that you get it. The ultimate demonstration: act in ways that prove that you listened and understood.