\[\boxed{\mathbf{1146}\mathbf{.}\mathbf{\ }}\]
\[\left( 6\frac{8}{11} \cdot \frac{4}{5} \right) \cdot 1\frac{1}{4} = \frac{74}{11} \cdot \frac{4}{5} \cdot \frac{5}{4} =\]
\[= \frac{74 \cdot 4 \cdot 5}{11 \cdot 5 \cdot 4} = \frac{74}{11} = 6\frac{8}{11}\]