The maximum vertical height to which a man can throw a ball is 136m...

Maximum height is achieved when the projection is along the vertical direction,

{H}_\max = \dfrac{{v}^{2}}{2g} = 136m

Now, for maximum range, angle of projection should be $45 °$. Therefore,

{R}_\max = \dfrac{{v}^{2}}{g} = 2{H}_\max

$= 2\left(136\right)$

$= 272m$