The ground state energy of $H$-atom is $13.6 \mathrm{eV}$. The energy needed to ionize $H$-atom from its second excited state is

Ionization energy is the energy required to remove an electron from a gaseous atom or ion.

for this case, initially, the electron is in $3^{rd}$ orbit and we know for $H$-atom ${\mathrm{E}}_{\mathrm{n}=3}=-1.51\mathrm{ }\mathrm{e}\mathrm{V}$ 

Hence ionization energy of the electron is $1.51\mathrm{ }\mathrm{eV}$