Co(NH3)4Br2]Cr is a coordination compound that contains a central cobalt (Co) ion coordinated to four ammonia (NH3) ligands and two bromide (Br-) ligands. The cobalt ion has a coordination number of six.

The isomerism exhibited by this compound is a combination of geometrical isomerism and ionization isomerism.

Geometrical Isomerism:
Geometrical isomerism occurs when there is restricted rotation around a bond, resulting in different spatial arrangements of the ligands. In this compound, the two bromide ligands are present in a cis configuration. This means that the two bromide ligands are located on adjacent sides of the coordination sphere. If they were present in a trans configuration, they would be located on opposite sides of the coordination sphere. Therefore, the compound exhibits geometrical isomerism.

Ionization Isomerism:
Ionization isomerism occurs when different ions are present inside and outside the coordination sphere. In this compound, the chromium (Cr) ion is present outside the coordination sphere. It is not directly bonded to the cobalt ion, but it is associated with the compound as an ion. If the chromium ion were replaced by another ion, such as a chloride ion (Cl-), the resulting compound would have a different ionization isomer. Therefore, the compound exhibits ionization isomerism.

Combination of Geometrical and Ionization Isomerism:
Since the compound exhibits both geometrical isomerism (due to the cis configuration of the bromide ligands) and ionization isomerism (due to the presence of the chromium ion outside the coordination sphere), the correct answer is option 'C' - geometrical and ionization isomerism.