To evaluate the determinant of a $2 \times 2$ matrix, write the determinant with vertical lines, then subtract the products of its diagonals. For example, to evaluate the determinant of the matrix $\begin{bmatrix} 4 & -2 \\ 3 & -1 \end{bmatrix}$, first write it as $\begin{vmatrix} 4 & -2 \\ 3 & -1 \end{vmatrix}$. Next, subtract the product of the bottom-left and top-right entries from the product of the top-left and bottom-right entries:

$(4)(-1) - (3)(-2)$

Simplifying this expression yields $-4 - (-6)$, which equals $-4 + 6 = 2$. Thus, the determinant is $2$. Similarly, the determinant of $\begin{bmatrix} -3 & -4 \\ -2 & 0 \end{bmatrix}$ is evaluated as $(-3)(0) - (-2)(-4)$, which simplifies to $0 - 8 = -8$.