Correct answer: (I) > (IV) > (III) > (II)
The correct order reflects the number of unpaired electrons in each complex, which determines the spin-only magnetic moment. [Cr(H2O)6]Br2 has the highest number of unpaired electrons due to its high-spin configuration, followed by (Et4N)2[CoCl4], which has fewer unpaired electrons, while Na3[Fe(C2O4)3] has a low-spin configuration with the least unpaired electrons, and Na4[Fe(CN)6] is fully paired, resulting in no magnetic moment.