Only one appointment can be checked out at a time. When you check out an appointment, the payment and receipt that's generated are both tied to the selected Client's record.
If a Client is paying for their appointment and another Client's appointment, you have to check out each separately.
If paying with a credit card, the card will need to be charged for each appointment. The card processing fees will be the same as one charge as long as the total charged is the same.
If paying with a check, add half to one appointment and the other half to the other. Include the same check number for each.