How to create a an insert trigger on
I assume SQL Server because of the getdate(). It would be something similar to

CREATE TRIGGER Management.PaymentsCreditCard
               ON Management.Payments
               AFTER INSERT,
                     UPDATE
BEGIN
  UPDATE Management.Payments
         SET CreditCardDetails = NULL
         FROM inserted
              INNER JOIN Management.PaymentMethods
                         ON PaymentMethods.PaymentMethodID = inserted.PaymentMethodID
         WHERE Payments.PaymentID = inserted.PaymentID
               AND PaymentMethods.Description = 'credit card';
END;


. (Just to give you the idea. I haven't tested it, it might need some adaption.)