The atomic mass of carbon is 12.011 g/mol. how many atoms of carbon have that exact mass? why?

An Avogadro's number (6.022 x 10^23) worth of carbon atoms have that exact mass.

12.011 is the MOLAR mass of carbon. It is the mass of 1 mole of carbon. 1 mole of anything contains 6.022 x 10^23 of that thing.