\(N = mg =\lambda( L - x ) g\)

\(fs _{\max }=\mu_{ s } N\)

\(fs _{\max }=(0.5)(\lambda)( L - x ) g\)

And also \(fs _{\max }= m _{ x } g\)

\(0.5 \lambda( L - x ) g =\lambda xg\)

\(\frac{ L - x }{2}= x\)

\(\frac{ L }{2}=\frac{3 x }{2} \Rightarrow x =\frac{ L }{3}=\frac{6}{3}=2 \,m\)