Match List - I with List - II and choose the correct answer.

List - I	List - II
(a) [Fe(CN)6]3-	(i) 5.92 BM
(b) [Fe(H2O)6]3+	(ii) 0 BM
(c) [Fe(CN)6]4-	(iii) 4.90 BM
(d) [Fe(H2O)6]2+	(iv) 1.73 BM

The correct matching option is (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii).

To determine the spin-only magnetic moment for each coordination complex, we need to find the oxidation state of the iron ($\mathrm{Fe}$) center, its d-electron configuration, whether the ligand is a strong-field ligand (causing pairing) or a weak-field ligand (no pairing), the number of unpaired electrons ($n$), and finally calculate the magnetic moment using the spin-only formula:
$\mu =\sqrt{n(n+2)} \mathrm{BM}$

Let us analyze each complex step-by-step:

(a) ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$:
1. Oxidation state of $\mathrm{Fe}$: Let $x$ be the oxidation state. $x+6(-1)=-3\Rightarrow x=+3$. So, we have ${\mathrm{Fe}}^{3+}$.
2. Electronic configuration of ${\mathrm{Fe}}^{3+}$ is $\left[\mathrm{Ar}\right]3d^5$.
3. Ligand: ${\mathrm{CN}}^{-}$ is a strong-field ligand. It causes pairing of electrons in the $t_{2g}$ orbitals.
4. Configuration after pairing: $t_{2g}^5{e}_g^0$, which leaves $n=1$ unpaired electron.
5. Magnetic moment:
$\mu =\sqrt{1(1+2)}=\sqrt{3}\approx 1.73 \mathrm{BM}$.
Hence, (a) matches with (iv).

(b) ${\left[\mathrm{Fe}{\left(H_{2}O\right)}_6\right]}^{3+}$:
1. Oxidation state of $\mathrm{Fe}$: $x+6\left(0\right)=+3\Rightarrow x=+3$. We have ${\mathrm{Fe}}^{3+}$.
2. Electronic configuration of ${\mathrm{Fe}}^{3+}$ is $\left[\mathrm{Ar}\right]3d^5$.
3. Ligand: $H_{2}O$ is a weak-field ligand. It does not cause pairing.
4. Configuration: $t_{2g}^3{e}_g^2$, which leaves $n=5$ unpaired electrons.
5. Magnetic moment:
$\mu =\sqrt{5(5+2)}=\sqrt{35}\approx 5.92 \mathrm{BM}$.
Hence, (b) matches with (i).

(c) ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$:
1. Oxidation state of $\mathrm{Fe}$: $x+6(-1)=-4\Rightarrow x=+2$. We have ${\mathrm{Fe}}^{2+}$.
2. Electronic configuration of ${\mathrm{Fe}}^{2+}$ is $\left[\mathrm{Ar}\right]3d^6$.
3. Ligand: ${\mathrm{CN}}^{-}$ is a strong-field ligand and causes pairing.
4. Configuration after pairing: $t_{2g}^6{e}_g^0$, which leaves $n=0$ unpaired electrons.
5. Magnetic moment:
$\mu =\sqrt{0(0+2)}=0 \mathrm{BM}$.
Hence, (c) matches with (ii).

(d) ${\left[\mathrm{Fe}{\left(H_{2}O\right)}_6\right]}^{2+}$:
1. Oxidation state of $\mathrm{Fe}$: $x+6\left(0\right)=+2\Rightarrow x=+2$. We have ${\mathrm{Fe}}^{2+}$.
2. Electronic configuration of ${\mathrm{Fe}}^{2+}$ is $\left[\mathrm{Ar}\right]3d^6$.
3. Ligand: $H_{2}O$ is a weak-field ligand. No pairing occurs.
4. Configuration: $t_{2g}^4{e}_g^2$, which leaves $n=4$ unpaired electrons.
5. Magnetic moment:
$\mu =\sqrt{4(4+2)}=\sqrt{24}\approx 4.90 \mathrm{BM}$.
Hence, (d) matches with (iii).

Combining the matches, we get:
(a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)