[Ni(CO)4]: In this complex nickel is in 0 oxidation state and valence electronic configuration is 4s23d8 . In presence of strong field ligand CO , two electrons present in 4s orbital get shifted to 3d orbital. Due to this, d orbital is completely filled in complex and all electrons are paired due to which it is diamagnetic. [NiCl4]2− : In this complex nickel is in +2 oxidation state and outermost electronic configuration is 3d8 and since Cl is weak field ligand it can't pair electrons in orbital of nickel due to which it is paramagnetic with two unpaired electrons. [CoF6]3− : In this complex cobalt is in +3 oxidation state and outermost electronic configuration is 3d6 and since fluoride is weak field ligand due to which it can't pair the electrons present in orbital of cobalt and complex is paramagnetic with four unpaired electrons. [Cu((NH)3)4(])2+ : In this complex copper is in +2 oxidation state and configuration is 3d9 and these electrons can't be paired anyhow therefore complex is paramagnetic with one unpaired electron. [Ni(CN]2−: : In this complex nickel is in +2 oxidation state and outermost electronic configuration is 3d8 and since CN is strong field ligand it will pair electrons in orbital of nickel due to which it is diamagnetic with two unpaired electrons.
Thus, [Ni(CO)4]and[Ni(CN)4(])2− are diamagnetic.