The weight of any person on the moon is about

Weight on moon $=\frac{1}{6} \times$ Weight on earth

ie., $m g_{m}=\frac{1}{6} m g_{e}$ or $g_{m}=\frac{g_{e}}{6}$

Force applied by person to lift $15 \mathrm{~kg}$ mass on earth, $\mathrm{F}=m g_{e}=\left(15 \mathrm{~g}_{e}\right) \mathrm{N}$

Let $M=$ maximum mass which can be lifted on the moon

$\therefore \mathrm{F}=\mathrm{Mg}_{m}$ or $\mathrm{M}=\frac{\mathrm{F}}{g_{m}}=\frac{15 g_{e}}{g_{m}}=\frac{15 g_{e}}{g_{e} / 6}=90 \mathrm{~kg} .$