Ionisation energy of He⁺ is I9.6x 10^-18 J atom^-1 . The energy of the first stationary state 

(n = 1) of Li²⁺ is

$\mathrm{En}=-13.6\frac{{\mathrm{Z}}^2}{{\mathrm{n}}^2}\mathrm{eV}$
$\mathrm{E}\propto {\mathrm{Z}}^2$
$\text{ Ionization energy of }{\mathrm{He}}^{+}=-{\mathrm{E}}_1=19.6\times {10}^{-18}\mathrm{J}{\text{ atom }}^{-1}\text{ (given) }$
${\mathrm{E}}_1\text{ for }{\mathrm{Li}}^{+2}=?$
$\frac{{\mathrm{E}}_{\left({\mathrm{He}}^{+}\right)}}{{\mathrm{E}}_{\left({\mathrm{Li}}^{+2}\right)}}=\frac{(2{)}^2}{(3{)}^2}=\frac{4}{9}$
${\mathrm{E}}_{\left({\mathrm{Li}}^{+2}\right)}=\frac{9}{4}\left(-19.6\times {10}^{-18}\right)=-44.1\times {10}^{-18}$
$=-4.41\times {10}^{-17}\mathrm{J}{\text{ atom }}^{-1}$