Simply replace the unfilled areas such as "" and "[date]" with your information.
Please let me take this opportunity to apologize for the [complaint] caused by my [source of complaint]. I did not mean for that to happen and I am very sorry. Thank you for bringing the situation to my attention so that I could correct the problem. As neighbors, it is important that we treat each other with respect and consideration, and I am sorry if I jeopardized that relationship.
I have [how problem was resolved]. This should prevent it from every happening again. If you find that the problem has recurred, please let me know and I will take care of it.