The number of geometrical isomers of the compound is
`C_(6)H_(5)-CH=CH-CH=CH-COOH`

Answer

To determine the number of geometrical isomers for the compound \( C_6H_5-CH=CH-CH=CH-COOH \), we will follow these steps:

### Step 1: Identify the double bonds
The compound contains two double bonds (alkenes) in the structure. The double bonds are located between the carbon atoms in the chain.

### Step 2: Determine the positions of the double bonds
The structure can be represented as follows:
- The first double bond is between the first and second carbon atoms.
- The second double bond is between the third and fourth carbon atoms.

### Step 3: Analyze the substituents on the double bonds
For geometrical isomerism (cis-trans isomerism) to occur, the double bonds must have different substituents. In this case:
- The first double bond has a phenyl group (\( C_6H_5 \)) on one side and a hydrogen atom on the other.
- The second double bond has a carboxylic acid group (\( COOH \)) on one side and a hydrogen atom on the other.

### Step 4: Count the number of geometrical isomers
Each double bond can exhibit cis and trans configurations:
- For the first double bond, we can have:
- **Cis**: \( C_6H_5 \) and \( H \) on the same side.
- **Trans**: \( C_6H_5 \) and \( H \) on opposite sides.

- For the second double bond, we can also have:
- **Cis**: \( COOH \) and \( H \) on the same side.
- **Trans**: \( COOH \) and \( H \) on opposite sides.

### Step 5: Calculate the total number of isomers
Since we have two double bonds, and each can independently be in either the cis or trans configuration, we can use the formula:
\[ \text{Total geometrical isomers} = 2^{n} \]
where \( n \) is the number of double bonds. Here, \( n = 2 \):
\[ \text{Total geometrical isomers} = 2^2 = 4 \]

### Conclusion
The total number of geometrical isomers for the compound \( C_6H_5-CH=CH-CH=CH-COOH \) is **4**.

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