To find the quotient of \(-96x^2\) divided by \(12x^2\), you can divide the coefficients and cancel the variable terms:
\[ \frac{-96x^2}{12x^2} = \frac{-96}{12} \cdot \frac{x^2}{x^2} \]
Calculating the coefficients:
\[ \frac{-96}{12} = -8 \]
And since \(\frac{x^2}{x^2} = 1\), the quotient simplifies to:
\[ -8 \cdot 1 = -8 \]
Thus, the final result is:
\[ \boxed{-8} \]