The total number of stereoisomers for `(A)` is `:`

Options

A. 6
B. 8
C. 4
D. 5

Explanation

To determine the total number of stereoisomers for compound (A), we need to consider both geometrical (cis/trans) and optical isomers due to the presence of chiral centers.

### Step-by-Step Solution:

1. **Identify the Structure of Compound (A)**:
- The compound has one double bond and two chiral centers.

2. **Count the Chiral Centers**:
- In this case, there are 2 chiral centers. However, we also need to analyze the double bond.

3. **Analyze the Double Bond**:
- The groups attached to the double bond are the same, which means we cannot use the formula \(2^n\) directly, where \(n\) is the number of stereocenters.

4. **Determine Geometrical Isomers**:
- For the double bond, we can have cis and trans configurations.
- The trans isomer can have different configurations at the chiral centers:
- Chiral center 3 (C3) can be in the S configuration, and chiral center 6 (C6) can be in the R configuration, leading to one meso form.
- The other configurations (C3 in R and C6 in S) will yield different optical isomers.
- Therefore, for the trans isomer, we have 3 optical isomers (1 meso + 2 different).

5. **Count Isomers for the Cis Isomer**:
- Similarly, for the cis isomer, we also have 3 optical isomers due to the same reasoning.

6. **Total Stereoisomers**:
- Adding the stereoisomers from both configurations:
- Trans isomer: 3 optical isomers
- Cis isomer: 3 optical isomers
- Total = 3 (trans) + 3 (cis) = 6 stereoisomers.

### Conclusion:
The total number of stereoisomers for compound (A) is **6**.

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