$\begin{align}  & 6r{{7}_{8}}={{511}_{9}} \\ & \text{converting both sides to decimal system} \\ & 6\times {{8}^{2}}+r\times {{8}^{1}}+7=5\times {{9}^{2}}+1\times {{9}^{1}}+1 \\ & 384+8r+7=405+9+1 \\ & 391+8r=415 \\ & 8r=24 \\ & r=3 \\\end{align}$