Solve the system $\left\{\begin{array}{l} 2x + y = -4 \\ 3x - 2y = -6 \end{array}\right.$ using Cramer's rule. First, evaluate the determinant $D$ using the coefficients of the variables: $D = \begin{vmatrix} 2 & 1 \\ 3 & -2 \end{vmatrix} = (2)(-2) - (1)(3) = -7$. Next, evaluate $D_x$ by replacing the $x$ coefficients with the constants $-4$ and $-6$: $D_x = \begin{vmatrix} -4 & 1 \\ -6 & -2 \end{vmatrix} = (-4)(-2) - (1)(-6) = 14$. Then, evaluate $D_y$ by replacing the $y$ coefficients with the constants: $D_y = \begin{vmatrix} 2 & -4 \\ 3 & -6 \end{vmatrix} = (2)(-6) - (-4)(3) = 0$. Now, find $x$ and $y$ using the formulas: $x = \frac{D_x}{D} = \frac{14}{-7} = -2$ and $y = \frac{D_y}{D} = \frac{0}{-7} = 0$. Write the solution as the ordered pair $(-2, 0)$. Finally, check the solution in both original equations to verify it is correct.