How do you know? Well, it is a carbon nucleus by specification. ALL carbon nuclei contain #6# #"protons"#, 6 positively charged, massive nuclear particles; i.e. #"Z, the atomic number"# #=# #6#. This what defines the atom as #"carbon"#.
But here the nucleus also contains #8# #"neutrons"#, 8 neutrally charged, massive nuclear particles. The sum of protons and neutrons constitutes MOST of the mass of the atom, hence we have a #""^14C# isotope. Most carbon nuclei contain only #6# #"neutrons"# to give the #""^12C# isotope. A few carbon atoms have #7# #"neutrons"# to give the #""^13C# isotope.