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I suggest that it is never appropriate to use a credit card that is not yours. Instead, your friend should call in and pay your invoice.
Just as you should not be giving your card number to anyone (unless paying a bill), you should actively avoid learning anyone else's card number. If their card were to be later compromised, you might end up needing to answer some very uncomfortable questions that could jeopardize a friendship.
If you do not have enough financial history to get a credit card, you might consider a secured card to start building that all-important credit rating and so that you will not have the same problem when AMF time comes around. The bank that holds your debit card may be willing to do some sort of deal where they issue you a secured card and then convert it to a credit card after a year's good payment history. That is how I got started.