(a) [Co(NH$_3$)$_6$]$^{3+$}: The complex has a central Co$^{3+}$ ion with 3d$^6$ electronic configuration. This implies that the ion undergoes \(d^2sp^3\) hybridization, resulting in an octahedral geometry. Since Co$^{3+}$ has no unpaired electrons, the complex is low-spin and diamagnetic. (b) [Ni(CO)$_4$]: The Ni$^{0}$ ion has a 3d$^8$ configuration. In this case, the CO ligands donate electron pairs and the Ni atom undergoes \(sp^3\) hybridization, forming a tetrahedral geometry. The complex has two unpaired electrons, making it paramagnetic.