1. **Statement of the problem:** Find the determinant of matrix $$A = \begin{bmatrix} 3 & 6 \\ 2 & 4 \end{bmatrix}$$. 2. **Formula used:** The determinant of a 2x2 matrix $$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$ is given by: $$\det(A) = ad - bc$$ 3. **Apply the formula:** Here, $$a=3$$, $$b=6$$, $$c=2$$, and $$d=4$$. Calculate: $$\det(A) = (3)(4) - (6)(2) = 12 - 12 = 0$$ 4. **Explanation:** The determinant is zero, which means the matrix is singular and does not have an inverse. **Final answer:** $$\boxed{0}$$