There is no oxygen in the given molecule.
This is a covalent compound, so we have to look at electronegativities. Electronegativity #(chi)# of an element is is a chemical property that describes the tendency of an atom to attract a shared pair of electrons (or electron density) towards itself. The element with the greatest electronegativity will have a negative oxidation number, and the element with the lowest electronegativity will have a positive oxidation number.
#chi_"H"=2.20#, and #chi_"C"=2.55#.
https://en.wikipedia.org/wiki/Electronegativity
Therefore, the hydrogen atoms each have an oxidation number of #+1#, for a total of #+6#. The two carbon atoms must have a combined oxidation number of #-6#, which means that each carbon atom has an oxidation number of #-3#.