To factor the expression \(-64xy - 96xy^2\), we can factor out the common factor, which is \(-8y\).
Starting with the expression:
\[ -64xy - 96xy^2 \]
We can factor out \(-8y\):
\[ -8y(8x + 12y) \]
Thus, the completed expression is:
\[ -8y(8x + 12y) \]
So, the completed expression you are looking for is:
\[ -8y(8x + 12y) \]