[PtCl2(NH3)4] Br2 and [PtBr2 (NH3)4]Cl2 have Ionization isomerism because when coordination compound having same molecular formula show difference in their ionization behavior and furnish different types of ions in solution the phenomenon is called ionization isomerism.

Coordination Isomers:
Coordination isomers are a type of isomerism in which the ligands and/or the coordination sphere of a complex ion undergo interchange with each other. In coordination isomers, the overall formula of the complex remains the same, but the ligands and counterions are interchanged.

Linkage Isomers:
Linkage isomers are a type of isomerism in which the ligands are attached to the metal ion through different atoms. In linkage isomers, the overall formula of the complex remains the same, but the ligands are attached to the metal ion through different atoms.

Ionization Isomers:
Ionization isomers are a type of isomerism in which the counterions of a complex ion are interchanged. In ionization isomers, the ligands and overall formula of the complex remain the same, but the counterions are interchanged.

Hydrate Isomers:
Hydrate isomers are a type of isomerism in which the complex ion exists in different hydrate forms. In hydrate isomers, the ligands and overall formula of the complex remain the same, but the water molecules coordinated to the metal ion are interchanged.

Explanation:
The compounds [PtCl2(NH3)4]Br2 and [PtBr2(NH3)4]Cl2 have the same overall formula, [PtX2(NH3)4]Y2, where X represents the ligands (chloride or bromide) and Y represents the counterions (bromide or chloride).

In [PtCl2(NH3)4]Br2, the chloride ligands are coordinated to the metal ion, and the bromide ions are the counterions. In [PtBr2(NH3)4]Cl2, the bromide ligands are coordinated to the metal ion, and the chloride ions are the counterions.

Therefore, the compounds differ only in the identity of the counterions (bromide and chloride). This interchanging of counterions corresponds to ionization isomerism, as the ligands and overall formula of the complex remain the same.

Hence, the correct answer is option C) Ionization isomers.