How many covalent bonds can carbon form with other atoms?

4 covalent bonds in normal situations however at higher energy levels carbon can bond form 6 covalent bonds.

Carbons electron configuration shows us 6 total electrons with 4 valence electrons. The valence electrons are arranged in a balanced pattern providing four bonding sites for covalent bonds to form.

However at higher energy levels all six of carbons electrons can be used to form covalent bonds.