How many covalent bonds does carbon form if each of its unpaired electrons participate in one bond?

First, you must know that a covalent bond if formed by an unpaired electron from each of the two atoms involved in the bond.

Then, the number of covalent bonds that an atom may form is equal to the number of unpaired electrons that the atom has.

Now you just need to know the number of unpaired electrons that an atom of carbon has.

It is a known fact that carbon has until four unpaired electrons.

This number comes from the electron configuration of carbon which is 1s2 2s2 2p2 and the fact that the two 2s electrons are promoted to the p level and then the carbon form 4 equal hybrid orbitals each with one unpaired electrons: 1s2 4sp3.

In conclusion, carbon has 4 unpaired electrons, each of which can form a covalent bond, for a total of 4 covalent bonds, if each unpaired electron participates in a in one covalent bond.