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There is no one size fits all answer to this question as the best way to respond might vary depending on the situation and the person you're dealing with. However if you feel that a person's apology is genuine and sincere a simple thank you for their effort may be enough to convey the acceptance that you are looking for. Ultimately it's important to remember that everyone makes mistakes and the ability to own up to one's mistakes and seek to make things right speaks volumes about someone's character.