$\Delta=\left|\begin{array}{ccc}6 \lambda & -3 & 3 \\ 2 & 6 \lambda & 4 \\ 3 & 2 & 3 \lambda\end{array}\right|=0$ (For No Solution)

$2 \lambda\left(9 \lambda^2-4\right)+(3 \lambda-6)+(2-9 \lambda)=0$

$18 \lambda^3-14 \lambda-4=0$

$(\lambda-1)(3 \lambda+1)(3 \lambda+2)=0$

$\Rightarrow \lambda=1,-1 / 3,-2 / 3$

For each $\lambda, \Delta_1=\left|\begin{array}{ccc}6 \lambda & -3 & 4 \lambda^2 \\ 2 & 6 \lambda & 1 \\ 3 & 2 & \lambda\end{array}\right| \neq 0$

Ans. $12\left(1+\frac{1}{3}+\frac{2}{3}\right)=24$