Solution:

Possible isomers for the complex compound [CuII(NH3)4][PtIICl4] can be determined by using geometrical isomerism.

1. Geometrical Isomerism

Geometrical isomerism occurs in compounds that have restricted rotation around a bond due to a double bond or a ring structure. This isomerism arises due to the difference in the spatial arrangement of atoms or groups around the double bond or in the ring structure.

2. Calculation of Isomers

The complex compound [CuII(NH3)4][PtIICl4] has the formula [Cu(NH3)4][PtCl4]. The copper ion has a d9 electronic configuration and is in the octahedral complex. The platinum ion is also in the octahedral complex.

There are two types of isomers possible for this complex compound:

- Geometrical isomers due to the presence of PtCl4.
- Optical isomers due to the presence of Cu(NH3)4.

a) Geometrical Isomers:

In this compound, the platinum ion is surrounded by four chloride ions, which can occupy either the cis or trans positions with respect to each other.

The possible isomers are:

- cis-[Cu(NH3)4][PtCl2(NH3)2]
- trans-[Cu(NH3)4][PtCl2(NH3)2]
- cis-[Cu(NH3)4][Pt(NH3)2Cl2]
- trans-[Cu(NH3)4][Pt(NH3)2Cl2]

b) Optical Isomers:

The copper ion is surrounded by four ammonia molecules, and since it is an octahedral complex, it can exist as a pair of enantiomers that are non-superimposable mirror images of each other.

The possible isomers are:

- (R,R)-[Cu(NH3)4][PtCl4]
- (S,S)-[Cu(NH3)4][PtCl4]

3. Total Number of Possible Isomers

The total number of possible isomers for the complex compound [CuII(NH3)4][PtIICl4] can be determined by multiplying the number of geometrical isomers with the number of optical isomers.

Therefore, the total number of possible isomers for the complex compound [CuII(NH3)4][PtIICl4] is 4 x 2 = 8.

However, two of these isomers are identical, namely cis-[Cu(NH3)4][Pt(NH3)2Cl2] and trans-[Cu(NH3)4][Pt(NH3)2Cl2]. Hence, the total number of possible isomers is 6.

Therefore, the correct answer is '6'.