The formula used here is:

Number of spectral lines $=\sum _{}^{}\left({\mathrm{n}}_2-{\mathrm{n}}_1\right)$

${\mathrm{n}}_2$= Highest energy level=6(fifth excited state)

${\mathrm{n}}_1$=Lowest energy level=2(first excited state)

Number of spectral lines

$=\sum _{}^{}\left(6-2\right)=10$

Number of spectral lines in ${\mathrm{He}}^{+}$ for transition from $\mathrm{n}=6$ to $\mathrm{n}=2$ are $10$