To match the electronic configurations with the metal complex ions, we need to determine the central metal ion's oxidation state, its d-electron count, the geometry of the complex, and whether it is a high-spin or low-spin complex based on the ligand field strength.

1. Analyze the electronic configurations in List-I:

• (P) $t_{2g}^6 e_g^0$: This represents a $d^6$ configuration. The subscript 'g' indicates an octahedral geometry. Since all 6 electrons are in the lower energy $t_{2g}$ orbitals (paired up), this is a low-spin complex, which implies a strong-field ligand.
• (Q) $t_{2g}^3 e_g^2$: This represents a $d^5$ configuration in an octahedral field. Since the electrons occupy the higher energy $e_g$ orbitals before the $t_{2g}$ orbitals are fully paired, this is a high-spin complex, implying a weak-field ligand.
• (R) $e^2 t_2^3$: This configuration has 5 d-electrons ($2+3=5$). The absence of the subscript 'g' indicates a tetrahedral geometry. In a tetrahedral field, the d-orbitals split into a lower energy $e$ set and a higher energy $t_2$ set. The filling ($e^2 t_2^3$) is consistent with a high-spin $d^5$ configuration, which is standard for tetrahedral complexes.
• (S) $t_{2g}^4 e_g^2$: This represents a $d^6$ configuration in an octahedral field. Since there are electrons in the $e_g$ orbitals while the $t_{2g}$ orbitals are not yet fully paired, this is a high-spin complex, implying a weak-field ligand.

2. Analyze the metal complex ions in List-II:

• (1) $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$:

  • Central metal ion: Fe. Atomic number = 26 ($[Ar] 3d^6 4s^2$).
  • Oxidation state of Fe is +2. So, we have $\mathrm{Fe}^{2+}$ ($d^6$ system).
  • Ligand: $\mathrm{H}_2O$ is a weak-field ligand.
  • Geometry: Octahedral (coordination number 6).
  • Spin: High-spin complex.
  • Electronic configuration for a high-spin $d^6$ octahedral complex is $t_{2g}^4 e_g^2$. This matches (S).

• (2) $\left[\mathrm{Mn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$:

  • Central metal ion: Mn. Atomic number = 25 ($[Ar] 3d^5 4s^2$).
  • Oxidation state of Mn is +2. So, we have $\mathrm{Mn}^{2+}$ ($d^5$ system).
  • Ligand: $\mathrm{H}_2O$ is a weak-field ligand.
  • Geometry: Octahedral.
  • Spin: High-spin complex.
  • Electronic configuration for a high-spin $d^5$ octahedral complex is $t_{2g}^3 e_g^2$. This matches (Q).

• (3) $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$:

  • Central metal ion: Co. Atomic number = 27 ($[Ar] 3d^7 4s^2$).
  • Oxidation state of Co is +3. So, we have $\mathrm{Co}^{3+}$ ($d^6$ system).
  • Ligand: $\mathrm{NH}_3$ is a strong-field ligand, especially with $\mathrm{Co}^{3+}$.
  • Geometry: Octahedral.
  • Spin: Low-spin complex.
  • Electronic configuration for a low-spin $d^6$ octahedral complex is $t_{2g}^6 e_g^0$. This matches (P).

• (4) $\left[\mathrm{FeCl}_4\right]^{-}$:

  • Central metal ion: Fe.
  • Oxidation state of Fe is +3. So, we have $\mathrm{Fe}^{3+}$ ($d^5$ system).
  • Ligand: $\mathrm{Cl}^-$ is a weak-field ligand.
  • Geometry: Tetrahedral (coordination number 4).
  • Spin: Tetrahedral complexes are typically high-spin.
  • Electronic configuration for a high-spin $d^5$ tetrahedral complex is $e^2 t_2^3$. This matches (R).

• (5) $\left[\mathrm{CoCl}_4\right]^{2-}$:

  • Central metal ion: Co.
  • Oxidation state of Co is +2. So, we have $\mathrm{Co}^{2+}$ ($d^7$ system).
  • Ligand: $\mathrm{Cl}^-$ is a weak-field ligand.
  • Geometry: Tetrahedral.
  • Spin: High-spin complex.
  • Electronic configuration for a high-spin $d^7$ tetrahedral complex is $e^4 t_2^3$. This does not match any configuration in List-I.

3. Final Matching:

• P $\rightarrow$ 3
• Q $\rightarrow$ 2
• R $\rightarrow$ 4
• S $\rightarrow$ 1

This corresponds to the option D.