He confessed having done a mistake.

The correct answer is C. acknowledged.

To acknowledge something is to admit that it is true or to recognize its existence. In this case, the man is acknowledging that he made a mistake.

The other options are incorrect because they do not accurately describe what the man is doing.

• To grant something is to give it or allow it to
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  happen.
• To concede something is to admit that you are wrong or that you have been defeated.
• To conceal something is
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  to hide it or keep it secret.

In this case, the man is not giving anything, admitting that he is wrong, or hiding anything. He is simply acknowledging that he made a mistake.