1. The problem asks to find the determinant of matrix $$A = \begin{pmatrix}0 & -2 \\ 6 & 30\end{pmatrix}$$. 2. The formula for the determinant of a 2x2 matrix $$\begin{pmatrix}a & b \\ c & d\end{pmatrix}$$ is: $$\det(A) = ad - bc$$ 3. Applying the formula to matrix $$A$$: $$\det(A) = (0)(30) - (6)(-2)$$ 4. Calculate the products: $$0 - (-12) = 0 + 12 = 12$$ 5. Therefore, the determinant of matrix $$A$$ is $$12$$. 6. The correct answer is option C: 12.