Why carbon atom cannot lose or gain electron to form octet
Carbon cannot gain or lose electrons. Carbon cannot for C4- because If it gains 4 electrons, it would be difficult for the nucleus with six protons to hold on to ten electrons, that is, four extra electrons.
Carbon cannot form C4+ because if it loses 4 electrons, it would require a large amount of energy to remove 4 electrons leaving behind a carbon cation with six protons in its nucleus holding on to just 2 electrons. Carbon overcomes this problem by sharing its valence electrons with other atoms of carbon or with atoms of other elements.