Hey @VIVIAN! When you copy a card from one board to another, you'll have the option to choose whether you want to keep the comments, labels, attachments, and custom fields or if you don't want them to be copied.
And when you move your card to another board, everything will be moved, including labels, attachments, comments, and Custom Fields. If you're experiencing a different issue when copying or moving your cards, please raise a ticket with us at https://trello.com/contact. We'll be more than happy to help!
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