How is the carbon able to …

Carbon may gain four electrons to attain a noble gas configuration. But in such a situation, it would be difficult for 6 protons to balance 10 electrons.
Carbon may lose four electrons to attain a noble gas configuration. But removing 4 electrons from a carbon atom would require too much energy and hence this won’t be possible in practical situations. Moreover, after losing four electrons the carbon atom would be left with just 2 electrons to balance 6 protons.

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