Verified Answer :

\(\frac{6}{13}:\frac{6}{12}=\frac{6}{13}*\frac{12}{6}= \boxed{\frac{12}{13}}\)

\(\frac{6}{13} / \frac{6}{12} = \frac{6}{13}* \frac{12}{6} = \frac{72}{78} = \frac{12}{13}\)
Therefore your answer is C. 12/13