For the absorption of visible light, presence of unpaired d-electrons is the necessity.
(a) In [Ni(CN)4]2−,Ni is present as Ni2+ Ni2+=[Ar]3d84s0
Since, in [Ni(CN)4]2−, no unpaired electron is present in d-orbitals, no unpaired electron is presen t in d-orbitals it does not absorb visible light.
(b) In [Cr(NH3)6]3+,Cr is present as Cr3+ Cr3+=[Ar]3d34s0 (Three unpaired electrons)
(c) In [Fe(H2O)6]3+,Fe is present as Fe2+.
[AI] 3d64s0 (Four unpaired electrons)
(d) In [Ni(H2O)6]2+,Ni is present as Ni2+. Ni2+=[Ar]3d84s0 (Two paired elections)
The complex given in option (b), (c), (d) have unpaired electrons, thus absorb visible light.