3d Geometry

If the shortest between the lines \({{x + \sqrt 6 } \over 2} = {{y - \sqrt 6 } \over 3} = {{z - \sqrt 6 } \over 4}\) and \({{x - \lambda } \over 3} = {{y - 2\sqrt 6 } \over 4} = {{z + 2\sqrt 6 } \over 5}\) is 6, then the square of sum of all possible values of \(\lambda\) is :