To multiply the expressions \( \sqrt{11} \) and \( 6\sqrt{7} \), we can use the property of multiplication of square roots and constants. Here are the steps:
\[ \sqrt{11} \cdot 6\sqrt{7} = 6 \cdot \sqrt{11} \cdot \sqrt{7} \]
Using the property that \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \):
\[ 6 \cdot \sqrt{11} \cdot \sqrt{7} = 6 \cdot \sqrt{11 \cdot 7} = 6 \cdot \sqrt{77} \]
Thus, the exact answer is:
\[ 6\sqrt{77} \]