How do I limit a number for a group of numerical entries totaled?

The maximum number that can be ordered is 24, however, the customer can order any variety of flavor up to 24 total.

For example, if the customer wants to order 3 Salted Caramel, 3 Earl Grey Tea, and 18 Raspberry Macarons, I would need the other fields to automatically zero out so that it doesn't let them enter any additional quantities because it has reached the max quantity of 24. 

Another example, if someone wants to order 24 Orange Blossom flavors then all other flavors would not allow an entry at all. 

How do I set this up?

You might try applying conditional logics , try with the option Update a form field value

Here is another guide that explain things in a more advanced way

http://www.jotform.com/help/268-How-to-Insert-Text-or-Mathematical-Calculation-into-a-field-using-a-Condition

If you need further help, then explain in details the scenario so we can help you to accomplish the form.