The energy of an electron of a hydrogen atom in the ground state is

$E_0=-13.6 \mathrm{eV}$

The energy of incoming photon = $12.75 \mathrm{eV}$

The energy of an electron in the excited state is

$-\frac{13.6}{n^2}=-13.6+12.75=-0.85 \mathrm{eV}$

$\Rightarrow n^2=\frac{13.6}{0.85}=16$

$\Rightarrow n=4$

No. of spectral lines = $\frac{n\left(n-1\right)}{2}$ = $6$