The first step in drawing the Lewis dot structure for ethane (C_2H_6C2H6) is to determine how many valence electrons are available for the molecule.
Since CC has 4 valence electrons, and each HH atoms contributes 1 valence electron, the total number of electrons will be
2*4 + 6*1 = 142⋅4+6⋅1=14 "e"^(-)e−
This means that the Lewis dot structure for C_2H_6C2H6 must account for 14 valence electrons, either through bonding between atoms, or through lone pairs.
So, the two CC atoms are placed in the center of the molecule. Each CC atom forms three covalent bonds with three HH atoms, with one aditional covalent bond being formed between the two CC atoms.
Each of these seven single bonds contains 2 electrons, which means that a total of
7 * 2 = 147⋅2=14 "e"^(-)e− were used for the C_2H_6C2H6 molecule.