Find the Noble Gas

For $\ 1s^2 2s^2 2p^6 3s^2 3p^6$ , the outermost shell is the third electron shell, which has $2+6=8$ valence electrons. Therefore, this choice represents the electron configuration of a noble gas ( $\text{Ar}$ )

For $\ 1s^2 2s^2 2p^5$ , the outermost shell is the second electron shell. The total number of electrons in this shell is $2+5=7.$ This is the electron configuration of $\text{F}.$

For $\ 1s^2 2s^2 2p^6 3s^1$ , the outermost shell is the third electron shell, which contains $1$ valence electron. This is the electron configuration of $\text{Na}.$

For $\ 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^8$ , the outermost shell is the fourth electron shell, which contains $2$ valence electrons. This is the electron configuration of $\text{Ni}.$

Simple: The outermost shell adds to 8 valence electrons - which is a noble gas.