Question

How does the carbon atom complete its octet?

Answer 1

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You probably didn't notice, but you posted your chemistry question in the biology section.
Next time when you ask a question, check if you're in the right section :)

Now to your question:

I attached
Carbon has an electron configuration of \(\large\sf1s^2\ 2s^2\ 2p^2\)
Carbon wants to have the electron configuration of a noble gas.
If you look at the periodic table ( http://www.ptable.com ), you can see that Neon is the closest one.
So to complete it's octet, carbon needs the electron configuration of neon.
The electron configuration of neon is \(\large\sf1s^2\ 2s^2\ 2p^6\)
As you can see, it's 4 electrons short \((\sf2p^2\) needs to be \(\sf2p^6)\)
Therefore, carbon will share 4 valence electrons with other atoms to make 4 covalent bonds to complete it's octet.

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