Visa ask # of days in China 12* with *3 nts in Hong Kong Answer 12 or 12 +3= 15 there?

Arriving in mainland 4/21/16 for 12 nights with an extension to Hong Kong for 3 nights - what is the correct answer? How many days in mainland with Hong Kong = 15.
American Citizens with Valid Passports trying to complete the Application correctly.

US citizens do not need to apply for Hong Kong right? but may need one to get back into mainland for the flight back to USA. Please advise how we should proceed. Is Hong Kong considered a part of PRC? if so we should answer 15 Days?