If the shortest between the lines (x+√ 6)/2=(y-√ 6)/3=(z-√ 6)/4 and (x-λ)/3=(y-2 √ 6)/4=(z+2 √ 6)/5 is 6, then the square of sum of all possible…

If the shortest between the lines $$\frac{x+\sqrt{6}}{2}=\frac{y-\sqrt{6}}{3}=\frac{z-\sqrt{6}}{4} \text { and } \frac{x-\lambda}{3}=\frac{y-2 \sqrt{6}}{4}=\frac{z+2 \sqrt{6}}{5} $$ is $\displaystyle 6$ , then the square of sum of all possible values of $\displaystyle \lambda$ is