The first step in drawing the Lewis dot structure for ethane (C2H6) is to determine how many valence electrons are available for the molecule.
Since C has 4 valence electrons, and each H atoms contributes 1 valence electron, the total number of electrons will be
2⋅4+6⋅1=14 e−
This means that the Lewis dot structure for C2H6 must account for 14 valence electrons, either through bonding between atoms, or through lone pairs.
So, the two C atoms are placed in the center of the molecule. Each C atom forms three covalent bonds with three H atoms, with one aditional covalent bond being formed between the two C atoms.
Each of these seven single bonds contains 2 electrons, which means that a total of
7⋅2=14 e− were used for the C2H6 molecule.