Two bodies of the same mass are connected with an inelastic string...

The velocity of $B$ just before the string is taut

${v}_{1} = \sqrt{u^{2} - 2gl} = \sqrt{6gl - 2gl} =2 \sqrt{gl}$

After the string is taut, both will move up with same speed, ${v}_{2} = \dfrac{mv1}{m + m} = \dfrac{v1}{2} = \sqrt{gl}$

By this time centre of mass in at $h = \dfrac{l}{2}$

A further rise in the centre of mass $= \dfrac{{v}_{2}2}{2g} = \dfrac{gl}{2g} = \dfrac{l}{2}$

Hence maximum height $= \dfrac{l}{2} + \dfrac{l}{2} = l$