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Ask what you can do to make it up to your friend. Offer a solution. Make a plan for the future.
One way to make amends is to simply ask how you can make it better. Of course, you can't fix a grievous mistake and completely reverse it; however, you may be able to do something to make it better, and the best way to figure out what is to defer to your friend. For instance, you could say, "I know I can't take back what I did, but is there any way I can make it up to you?" If your friend doesn't have a suggestion, you can offer your own solution. That solution can be a grand gesture to show you care, or it can be you making sure you show up in the ways you need for your friend. For example, maybe you could send your friend flowers or a graduation gift if you missed her graduation. One way you can make amends is to talk about how you can do things differently in the future. That way, your friend can feel reassured that the same situation won't occur again, and he will be more likely to accept your apology. For example, you could say, "The next time we go out together, we can talk about what to do ahead of time. That way, I won't disappoint you by leaving you alone for too long."