$\frac{1}{3}\cdot \left(3^{12}\cdot 27:9^6\right)=\frac{1}{3}\cdot \left(3^{12}\cdot 3^3:{\left(3^2\right)}^6\right)=\frac{1}{3}\cdot \left(3^{12}\cdot 3^3:3^{12}\right)=\frac{1}{3}\cdot \left(3^{12+3-12}\right)=\frac{1}{3}\cdot \left(3^3\right)=\frac{1}{3}\cdot 27=9$