The correct statement(s) about the compound
`H_(3)C(HO)HC-CH=CH-CH(OH)CH_(3) (X)` is/are

Options

A. The total number os steoisomers possible for `(X)` is 6.
B. The total number of diastereomers possible for `(X)` if 3.
C. If the stereochemistry about the double bond in `(X)` is trans, the number of enantiomers possible for `(X)` is 4
D. If the stereochemistry about the double bond is cis, then number of enantiomers possible for `(X)` is 2.

Answer

To solve the question regarding the compound \( H_3C(HO)HC-CH=CH-CH(OH)CH_3 \) (denoted as X), we will analyze the statements given about the compound step by step.

### Step 1: Determine the Structure of the Compound
First, we need to visualize the structure of the compound X. The compound can be represented as follows:

```
HO OH
| |
H3C-C-CH=CH-C-CH3
```

This structure indicates that there are hydroxyl (OH) groups attached to the carbon chain, and there is a double bond between the fourth and fifth carbon atoms.

### Step 2: Analyze Stereoisomers
Next, we will analyze the stereoisomers of the compound. We need to consider both the cis and trans configurations of the double bond.

1. **Cis Configuration**:
- In the cis configuration, the substituents on the double bond are on the same side. This configuration can lead to one meso compound and two enantiomers.

2. **Trans Configuration**:
- In the trans configuration, the substituents on the double bond are on opposite sides. This configuration can also lead to one meso compound and two enantiomers.

Thus, for both configurations, we can summarize:
- **Cis Configuration**: 3 stereoisomers (1 meso + 2 enantiomers)
- **Trans Configuration**: 3 stereoisomers (1 meso + 2 enantiomers)

### Step 3: Total Stereoisomers
Adding the stereoisomers from both configurations, we find:
- Total stereoisomers = 3 (cis) + 3 (trans) = 6 stereoisomers.

### Step 4: Analyze Diastereomers
Next, we need to determine the number of diastereomers. Diastereomers are stereoisomers that are not mirror images of each other.
- From our previous analysis, we can see that there are more than 3 diastereomers when considering both cis and trans configurations.

### Step 5: Analyze Enantiomers
Now, we will analyze the number of enantiomers:
- For the cis configuration, there are 2 enantiomers.
- For the trans configuration, there are also 2 enantiomers.

Thus, the total number of enantiomers is 2 for each configuration.

### Step 6: Conclusion on Statements
Now we can evaluate the statements:
- **Statement A**: Total number of stereoisomers possible for X is 6. **(Correct)**
- **Statement B**: Total number of diastereomers possible for X is 3. **(Incorrect)**
- **Statement C**: If the stereochemistry about the double bond in X is trans, the number of enantiomers possible is 4. **(Incorrect)**
- **Statement D**: If the stereochemistry about the double bond is cis, then the number of enantiomers possible for X is 2. **(Correct)**

### Final Answer
The correct statements about the compound X are A and D.

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