The outer shell of a carbon atom can hold a maximum of eight electrons. This is due to the octet rule, which states that atoms tend to form bonds in such a way that they achieve a full outer shell of electrons, typically eight. Carbon, which has an atomic number of 6, has two electrons in its inner shell and four electrons in its outer shell. To achieve a stable configuration, carbon can share, gain, or lose electrons to fill its outer shell, thus allowing it to attain the full complement of eight electrons.
In this case, the maximum capacity for the outer shell is what allows carbon to form stable covalent bonds with various other atoms, fulfilling the octet rule and establishing a tendency towards stability.