1. **Problem:** Solve the equation given by the determinant for part (a): $$\begin{vmatrix} 6 & 2 \\ 3 & x \end{vmatrix} = 0$$ 2. **Formula:** The determinant of a 2x2 matrix \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\) is calculated as: $$\det = ad - bc$$ 3. **Apply the formula:** $$6 \cdot x - 2 \cdot 3 = 0$$ 4. **Simplify:** $$6x - 6 = 0$$ 5. **Solve for \(x\):** $$6x = 6$$ $$x = \frac{6}{6} = 1$$ 6. **Answer:** The solution to the determinant equation is \(x = 1\).