1. **State the problem:** Find the determinant of the given 2x2 matrix $$\begin{bmatrix}-9 & 6 \\ 4 & -8\end{bmatrix}$$ 2. **Formula for determinant of a 2x2 matrix:** For a matrix $$\begin{bmatrix}a & b \\ c & d\end{bmatrix},$$ the determinant is calculated as $$\det = ad - bc$$ 3. **Apply the formula:** Here, $a = -9$, $b = 6$, $c = 4$, and $d = -8$. $$\det = (-9)(-8) - (6)(4)$$ 4. **Calculate each product:** $$(-9)(-8) = 72$$ $$6 \times 4 = 24$$ 5. **Subtract the products:** $$\det = 72 - 24 = 48$$ 6. **Interpretation:** The determinant of the matrix is 48, which means the matrix is invertible and its area scaling factor is 48. **Final answer:** $$\boxed{48}$$