Introduction:
In order to determine the geometries of the ammonia complexes of Ni2, Pt2, and Zn2, we need to consider the electronic configurations and bonding preferences of these metal ions.

Ni2:
- Electronic configuration of Ni2: [Ar] 3d8
- The electronic configuration suggests that Ni2 has a d8 configuration, which means it can accommodate up to 8 electrons in its d orbitals.
- Ammonia, NH3, is a strong ligand that forms coordinate bonds with the metal ion.
- In the case of Ni2, it can form a maximum of 6 coordinate bonds with ammonia due to its d8 configuration.
- Therefore, the geometry of the ammonia complex of Ni2 is octahedral. (A)

Pt2:
- Electronic configuration of Pt2: [Xe] 4f14 5d9 6s1
- The electronic configuration suggests that Pt2 has a d9 configuration, which means it can accommodate up to 9 electrons in its d orbitals.
- Ammonia, NH3, is a strong ligand that forms coordinate bonds with the metal ion.
- In the case of Pt2, it can form a maximum of 4 coordinate bonds with ammonia due to its d9 configuration.
- Therefore, the geometry of the ammonia complex of Pt2 is square planar. (B)

Zn2:
- Electronic configuration of Zn2: [Ar] 3d10 4s2
- The electronic configuration suggests that Zn2 has a d10 configuration, which means it can accommodate up to 10 electrons in its d orbitals.
- Ammonia, NH3, is a strong ligand that forms coordinate bonds with the metal ion.
- In the case of Zn2, it can form a maximum of 4 coordinate bonds with ammonia due to its d10 configuration.
- Therefore, the geometry of the ammonia complex of Zn2 is tetrahedral. (C)

Summary:
- The geometries of the ammonia complexes of Ni2, Pt2, and Zn2 are octahedral, square planar, and tetrahedral, respectively.
- This is determined by considering the electronic configurations and bonding preferences of these metal ions.