To simplify the expression \(\sqrt{14}(-8 - \sqrt{2})\), we will distribute \(\sqrt{14}\) to both terms inside the parentheses:
\[ \sqrt{14}(-8) + \sqrt{14}(-\sqrt{2}) \]
This gives:
\[ -8\sqrt{14} - \sqrt{14}\sqrt{2} \]
Since \(\sqrt{14} \sqrt{2} = \sqrt{28}\), we can further simplify the expression:
\[ -8\sqrt{14} - \sqrt{28} \]
Thus, the simplified expression is:
\[ -8\sqrt{14} - \sqrt{28} \]
If you want to simplify \(\sqrt{28}\) further, note that \(\sqrt{28} = \sqrt{4 \cdot 7} = 2\sqrt{7}\). So, the expression can be written as:
\[ -8\sqrt{14} - 2\sqrt{7} \]
So the final answer is:
\[ -8\sqrt{14} - 2\sqrt{7} \]