To determine which complex compound is diamagnetic, let's analyze the electronic configuration of the metal ions in each compound.
(i) [Co(NH3)6]Cl3: Cobalt has a configuration of [Ar] 3d7 4s2. In this complex, cobalt has lost three electrons, resulting in the configuration [Ar] 3d6. Since it has completely filled d-orbitals (d6), it's diamagnetic.
(ii) [Ni(NH3)6]Cl2: Nickel has a configuration of [Ar] 3d8 4s2. In this complex, nickel has lost two electrons, resulting in the configuration [Ar] 3d8. It has unpaired electrons, so it's paramagnetic.
(iii) [Cr(H2O)6]Cl3: Chromium has a configuration of [Ar] 3d5 4s1. In this complex, chromium has lost three electrons, resulting in the configuration [Ar] 3d3. It has unpaired electrons, so it's paramagnetic.
(iv) [Fe(H2O)6]Cl2: Iron has a configuration of [Ar] 3d6 4s2. In this complex, iron has lost two electrons, resulting in the configuration [Ar] 3d6. It has completely filled d-orbitals (d6), so it's diamagnetic.
So, among the given options, the complex compound that is diamagnetic is option (d) - (iv) [Fe(H2O)6]Cl2.