Noble gas configuration means the ion must have the same electron configuration as a noble gas:

Noble gases and their electron counts are: $2, 10, 18, 36, 54, 86$ corresponding to He, Ne, Ar, Kr, Xe, Rn.

Find electrons in each ion by subtracting the positive charge from atomic number.

(i) $\mathrm{Sr}^{2+}$, $Z=38$ $38-2=36$ $36 = \text{Kr configuration}$ So, $\mathrm{Sr}^{2+}$ has noble gas configuration.

(ii) $\mathrm{Cs}^{+}$, $Z=55$ $55-1=54$ $54 = \text{Xe configuration}$ So, $\mathrm{Cs}^{+}$ has noble gas configuration.

(iii) $\mathrm{La}^{2+}$, $Z=57$ $57-2=55$ $55 \neq \text{noble gas electron count}$ So, $\mathrm{La}^{2+}$ does not have noble gas configuration.

(iv) $\mathrm{Pb}^{2+}$, $Z=82$ $82-2=80$ $80 \neq \text{noble gas electron count}$ So, $\mathrm{Pb}^{2+}$ does not have noble gas configuration.

(v) $\mathrm{Yb}^{2+}$, $Z=70$ $70-2=68$ $68 \neq \text{noble gas electron count}$ So, $\mathrm{Yb}^{2+}$ does not have noble gas configuration.

(vi) $\mathrm{Fe}^{2+}$, $Z=26$ $26-2=24$ $24 \neq \text{noble gas electron count}$ So, $\mathrm{Fe}^{2+}$ does not have noble gas configuration.

Count the ions with noble gas configuration

They are: $\mathrm{Sr}^{2+},\ \mathrm{Cs}^{+}$

Total number: $2$

Comparison with stored answer

Stored correct answer = $2$.

Our derived answer also = $2$, so they agree.