1. Identify the type of reaction

   The reaction is: $\ce{Cl^. + CH4 -> A + B}$

   A chlorine radical reacts with methane. This is a free-radical substitution propagation step.

2. What does chlorine radical do to methane?

   A chlorine radical abstracts one hydrogen atom from methane: $\ce{Cl^. + CH4 -> HCl + CH3^.}$

   Here:

   • chlorine radical takes one H atom from methane,
   • methane becomes methyl radical, $\ce{CH3^.}$,
   • and $\ce{HCl}$ is formed.

3. Match with the options

   The products are: $A = \ce{CH3^.}, \quad B = \ce{HCl}$

   This corresponds to Option C.

4. Check other options briefly

   • A: $\ce{C2H6}$ and $\ce{Cl2}$ — not formed in this elementary step.
   • B: radical written is not correct for this step, and $\ce{H2}$ is not formed.
   • D: $\ce{C2H6}$ and $\ce{HCl}$ — ethane is not formed directly here.

Therefore, the correct answer is C.