To determine the change in oxidation number of carbon in the given reaction,$\\$we need to calculate the oxidation states of carbon in both the reactant and the product.$\\$The reaction is:$\\$CH$_4(g) + 4$Cl$_2(g) \rightarrow$CCl$_4(l) + 4$HCl$(g) \\$Step 1: Determine the oxidation state of carbon in $$CH$_4. \\$• In $$CH$_4,$ hydrogen has an oxidation state of $+1. \\$• Let the oxidation state of carbon be $x. \\$• The sum of oxidation states in $$CH$_4$ is zero (since it is a neutral molecule):$\\ x + 4(+1) = 0 \\ x + 4 = 0 \\ x = -4 \\$Step 2: Determine the oxidation state of carbon in $$CCl$_4. \\$• In $$CCl$_4,$ chlorine has an oxidation state of $-1. \\$• Let the oxidation state of carbon be $y. \\$• The sum of oxidation states in $$CCl$_4$ is zero:$\\ y + 4(-1) = 0 \\ y - 4 = 0 \\ y = +4 \\$Step 3: Calculate the change in oxidation number of carbon.$\\$• The oxidation state of carbon changes from $-4$ in $$CH$_4$ to $+4$ in $$CCl$_4. \\$• The change in oxidation number is:$\\ +4 - (-4) = +4 + 4 = +8 \\$Therefore, the change in oxidation number of carbon is from $-4$ to $+4. \\$This corresponds to Option 2.