For case-I : $2^{\text {nd }}$ equation $s=u t+\frac{1}{2}$ at $^{2}$

$h =- u (6)+\frac{1}{2}\, g (6)^{2}$

$H =-6 u +18\,g \ldots$ $(i)$

For case-II $: h = u (1.5)+\frac{1}{2}\, g (1.5)^{2}$

$h =1.5 u +\frac{2.25 g }{2} \ldots$ $(ii)$

Multiplying equation $(ii)$ by $4$ we get

$4 h =6 u +4.5\, g \ldots .$ $(iii)$

equation $(i)$ $+$ equation $(iii)$ we get $5 h =22.5 g$

$h =4.5 g \ldots$ $(iv)$

For case$-III$

$h =0+\frac{1}{2} gt ^{2} \ldots$ $(v)$

Using equation $(4)$and equation $(5)$

$4.5 g=\frac{1}{2} g t^{2}$

$t ^{2}=9 \Rightarrow t =3 s$