In [NiCl4]2− oxidation state of Ni is +2 and it have
↿⇂↿⇂↿⇂ ↿↿
8 electrons in d shell which is arranged as above, it has 2 unpaired electrons, so it is paramagnetic.
In [Ni(CO)4] oxidation state of Ni is 0 and two electron from 4s is pushed into 3d oribtal.
↿⇂↿⇂↿⇂ ↿⇂↿⇂
It has fully filled d-orbital.
∴[Ni(CO)4] is diamagnetic