If a carbon atom is bonded to two hydrogen atoms and two carbon atoms which type of bond must exist between the carbon atoms

Carbon to carbon bond is nonpolar covalent since the difference of their electronegativity’s is 0. Carbon has an electronegativity of 2.5. 2.5 - 2.5 is 0 making the bond between those two atoms nonpolar covalent. I hope I answered your question.

it is the most commonly accepted one