1. Stating the problem: Calculate the determinant of the matrix $$\begin{bmatrix}4 & 4 \\ 4 & -4\end{bmatrix}.$$\n\n2. Recall the formula for the determinant of a 2x2 matrix $$\begin{bmatrix}a & b \\ c & d\end{bmatrix}$$ is $$ad - bc.$$\n\n3. Substitute values: $$a=4, b=4, c=4, d=-4.$$\n\n4. Calculate: $$\det = (4)(-4) - (4)(4) = -16 - 16 = -32.$$\n\n5. Final answer: The determinant of the matrix is $$-32.$$