jmc

Multiplying, we see that $6_8\cdot 7_8=42_{10}=52_8.$ Written out, \begin{array}{@{}c@{\;}c@{}c@{}c} && & 6_8 \\ & \times & & 7_8 \\ \cline{2-4} & & 5 & 2_8 \\ \end{array} Thus, the answer is $\boxed{52_8}.$