Free Radical Reaction of Methane and Chlorine
OK, let's focus on the stoichiometry of your last 4 equations:

$\ce{2 CH4 + 2 Cl2 -&gt; 2 HCL + 2 CH3 + 2 Cl~~~~}$  this looks OK

$\ce{2 Cl + 2 CH3 -&gt; 2 CH3Cl~~~~~~~~~~~}$ this looks OK

$\ce{2 CH3Cl + 2 CH3Cl -&gt; 1 C2H6 + 1 Cl2~~~~}$ this should be $\ce{1 CH3Cl + 1 CH3Cl -&gt; 1 C2H6 + 1 Cl2}$

$\ce{2 HCl -&gt; 2 H2 + 2 Cl2~~~~~~~}$ this should be $\ce{2 HCl -&gt; 1 H2 + 1 Cl2}$

I'm not sure I agree with all of your chemical reactions, but at least now you don't wind up with more chlorine then you started with.