smc

Call the number $\overline{abc}$ in base 7. Then, $49a+7b+c=81c+9b+a$. (Breaking down the number in base-form). After combining like terms and moving the variables around, $48a=2b+80c$,$b=40c-24a=8(5c-2a)$. This shows that $b$ is a multiple of 8 (we only have to find the middle digit under one of the bases). Thus, $b=0$ (since 8>6, the largest digit in base 7). Select $\boxed{0}$ as our answer.