The 6 is the atomic number of carbon:
This number tells us how many PROTONS there are in the atom = 6 protons
Because there are 6 protons in the atom, there must be 6ELECTRONS in the atom
The number 13 is the atomic mass of the atom.
Atomic mass is equal to number of protons + number of neutrons. Because we know that we ahve 6 protons, to get to 13 we have to have 7 NEUTRONs
Number of protons = 6
number of neutrons = 7
number of electrons = 6