Carbon is a non metal with atomic number 6.
electronic configuration of carbon in ground state:
1s2 2s2 2p2.
To get the octet in its outer shell it has to gain 4 more electrons to form C4- ion. the electronegativity of carbon is only 2.5 and its nucleus has only 6 protons. therefore its difficult for a nucleus with 6 protons to hold 10 electrons.
Hence carbon cannot form C4- ions so easily.
If carbon looses 4 electrons from its outer shell, it has to form C 4 + ion. This requires huge amount of energy which is not available normally.
Therefore C4+ formation also is a remote possibility.
Carbon has to satisfy tetravalency, by sharing electrons with other atoms.so it has to form 4 covalent bonds either with its own atoms or atoms of other elements.