JEE 2023 — Mathematics PYQ

Let $S$ be the set of values of $\lambda$, for which the system of equations:

$6\lambda x-3y+3z=4{\lambda }^2$

$2x+6\lambda y+4z=1$

$3x+2y+3\lambda z=\lambda$

has no solution. Then $12{\sum }_{\lambda \in S}|\lambda |$ is equal to ____.