- A) \( {[MnBr}_4]^{2-} \): The \( {Mn}^{2+} \) ion has an \( 3d^5 \) configuration, leading to an \( sp^3 \) hybridization with a diamagnetic behavior due to the pairing of electrons. Hence, it corresponds to (III).
- B) \( {[FeF}_6]^{3-} \): The \( {Fe}^{3+} \) ion has a \( 3d^5 \) configuration, resulting in \( sp^2d^2 \) hybridization with paramagnetic behavior. Hence, it corresponds to (II).
- C) \( {[Co(C}_2{O}_4)_3]^{3-} \): The \( {Co}^{3+} \) ion leads to a \( 3d^6 \) configuration, requiring \( d^2sp^3 \) hybridization with diamagnetic behavior. Hence, it corresponds to (I).
- D) \( [Ni(CO)_4] \): The \( {Ni}^{2+} \) ion has a \( 3d^8 \) configuration with \( sp^3 \) hybridization and paramagnetic behavior. Hence, it corresponds to (IV). Thus, the correct matching is (A)-(III), (B)-(II), (C)-(I), (D)-(IV).