`underset("Tollen's test")underset("Gives positive")underset(darr)(C_(3)H_(6)O(A))overset(PhCHO)underset(OH^(-)//Delta)rarrB`
Product B is :

Options

A. `Ph-CH=underset(CH_(3))underset("| ")"C "-CH_(3)`
B.
C. `Ph-overset(CH_(3))overset("| ")"C "=CH-Ph`
D. `Ph-CH=underset(CH_(3))underset("| ")"C "-CHO`

Answer

To solve the problem, we need to identify the product B formed when a compound with the formula C₃H₆O (which gives a positive Tollen's test) reacts with benzaldehyde (PhCHO) in the presence of hydroxide ions (OH⁻) and heat.

### Step-by-Step Solution:

1. **Identify the structure of C₃H₆O**:
- Since C₃H₆O gives a positive Tollen's test, it indicates that it is either an aldehyde or an alpha-hydroxy ketone. The only possible aldehyde with three carbon atoms is propanal (CH₃CH₂CHO).

2. **Understanding Tollen's Test**:
- Tollen's reagent is used to detect aldehydes. A positive result indicates the presence of an aldehyde functional group, which can be oxidized to a carboxylic acid.

3. **Reaction with Benzaldehyde**:
- The reaction involves propanal (C₃H₆O) reacting with benzaldehyde (PhCHO) in the presence of hydroxide ions (OH⁻) and heat. This is indicative of an aldol condensation reaction.

4. **Formation of Carbanion**:
- The hydroxide ion (OH⁻) abstracts a proton from the alpha carbon of propanal, creating a carbanion. This carbanion is then nucleophilic and can attack the carbonyl carbon of benzaldehyde.

5. **Nucleophilic Attack**:
- The carbanion formed from propanal attacks the carbonyl carbon of benzaldehyde, resulting in the formation of a β-hydroxy aldehyde.

6. **Dehydration**:
- Upon heating, the β-hydroxy aldehyde undergoes dehydration (loss of water) to form an α,β-unsaturated aldehyde.

7. **Final Product B**:
- The final product after dehydration will be an α,β-unsaturated aldehyde, specifically cinnamaldehyde (CH₃CH=CHCHO).

### Conclusion:
The product B formed from the reaction is **cinnamaldehyde**.