It's the Amazing Math Trick!

Some friends were over for pizza the other day, and one of the kids (an eighth grader) said she wanted to show me a math trick. I said sure, and so she asked me to pick any number. I mentally chose my favorite number, but then she could somehow tell that I had made an unusual choice. So, she told me to pick a whole number. I accepted her new constraint and said I had picked a new number. Again she was still suspicious, so she insisted that I pick a positive whole number. Deflated, I chose accordingly and followed along as she had me:
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double it,
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add 6,
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divide by 2, and then
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subtract the original number