Is there a case when an atom of some element (e.g. carbon) does not have its expected number of protons (e.g. 6)?
A carbon atom has 6 neutrons. How many protons are present in the nucleus of a carbon atom?
  


Obviously this wording would make any astute student say the answer is 6 since carbon by definition has 6 protons. You are correct, elements are defined by their number of protons. Key word being defined, changing the number of protons changes the element.

I believe the key here that your book is getting at is you only know that you have an atom from a carbon sample that has 6 neutrons but nothing else. I think the question is trying to evaluate if you are aware that proton numbers are independent of neutron numbers thus knowing there are 6 neutrons does not help you determine protons, especially given one of the options is:


  D. Can't tell; more information is required.


If this is what they wanted then it was a very poor choice of words to say a carbon atom in the question then ask for number of protons. They should have said:


  Given an atom (or nucleus) with 6 neutrons, how many protons are present in the nucleus of the atom?