Total number of ions from the following with noble gas configuration is
$$Sr^{2+}$$ (Z = 38), $$Cs^+$$ (Z = 55), $$La^{2+}$$ (Z = 57), $$Pb^{2+}$$ (Z = 82), $$Yb^{2+}$$ (Z = 70) and $$Fe^{2+}$$ (Z = 26)

We need to determine how many of the given ions have noble gas configuration.

A noble gas configuration means the ion's electron configuration matches that of a noble gas (He, Ne, Ar, Kr, Xe, Rn).

$$Sr^{2+}$$ (Z = 38): $$Sr$$ has configuration $$[Kr]5s^2$$. Removing 2 electrons gives $$[Kr]$$ — 36 electrons. This is the krypton noble gas configuration. Yes.

$$Cs^+$$ (Z = 55): $$Cs$$ has configuration $$[Xe]6s^1$$. Removing 1 electron gives $$[Xe]$$ — 54 electrons. This is the xenon noble gas configuration. Yes.

$$La^{2+}$$ (Z = 57): $$La$$ has configuration $$[Xe]5d^1 6s^2$$. Removing 2 electrons gives $$[Xe]5d^1$$ — 55 electrons. This is NOT a noble gas configuration (it has one extra d-electron beyond Xe). No.

$$Pb^{2+}$$ (Z = 82): $$Pb$$ has configuration $$[Xe]4f^{14}5d^{10}6s^2 6p^2$$. Removing 2 electrons (from 6p) gives $$[Xe]4f^{14}5d^{10}6s^2$$ — 80 electrons. This is NOT a noble gas configuration. No.

$$Yb^{2+}$$ (Z = 70): $$Yb$$ has configuration $$[Xe]4f^{14}6s^2$$. Removing 2 electrons gives $$[Xe]4f^{14}$$ — 68 electrons. This is NOT a noble gas configuration. No.

$$Fe^{2+}$$ (Z = 26): $$Fe$$ has configuration $$[Ar]3d^6 4s^2$$. Removing 2 electrons gives $$[Ar]3d^6$$ — 24 electrons. This is NOT a noble gas configuration. No.

Only $$Sr^{2+}$$ and $$Cs^+$$ have noble gas configurations.

The answer is 2.