Ethane is two carbon atoms, single-bonded together, with three hydrogens on EACH of those two carbon atoms.
Carbon atoms bring 4 valence electrons each – that makes 8 total valence electrons brought by carbon to this molecule. Hydrogen atoms bring 1 valence electrons each – that makes 6 total valence electrons brought by hydrogen. Therefore, we have 8+6 = 14 valence electrons to work with in this Lewis Structure.
Each of the single bonds in the molecule ‘uses up’ two electrons; that’s actually all of the electrons we are allotted; there are no “lone pairs” of electrons on this molecule.