As long as the person has your credit card statement and account number they can make a payment through either there debit card or through a check or money order to your credit card bill.
If they have your statement and are paying through debit card there should be a form on the statement to fill out their debit card details for payment.
If the other person is paying your credit card bill through a check or money order the person just needs to fill out the check or money order normally and sign there name on the check and put your account number on the memo section of the check or money order for the payment to go through.