a) $\left[\mathrm{S}_2 \mathrm{O}_3\right]^{2-}$ is a strong reducing agent, so a $\rightarrow$ III.
b) $\mathrm{H}_2 \mathrm{O}_2$ can disproportionate in the presence of $\mathrm{Mn}^{2+}$, so b $\rightarrow$ IV.
c) $\mathrm{H}_2 \mathrm{S}$ is a toxic gas, so c $\rightarrow$ II.
d) $\mathrm{S}_2$ is paramagnetic, so d $\rightarrow$ I.
So, the correct option is D) $(\mathrm{a} \rightarrow \mathrm{III}),(\mathrm{b} \rightarrow \mathrm{IV}),(\mathrm{c} \rightarrow \mathrm{II}),(\mathrm{d} \rightarrow \mathrm{I})$.
Here is why:
a) $\left[\mathrm{S}_2 \mathrm{O}_3\right]^{2-}$ is a strong reducing agent because it can donate electrons to other substances in a chemical reaction.
b) $\mathrm{H}_2 \mathrm{O}_2$ can disproportionate in the presence of $\mathrm{Mn}^{2+}$, which means it can react with itself to produce different substances, one of which is oxidized and the other is reduced.
c) $\mathrm{H}_2 \mathrm{S}$ is a toxic gas, which means it is harmful or lethal to living organisms.
d) $\mathrm{S}_2$ is paramagnetic, which means it has unpaired electrons and is attracted to a magnetic field.