A mixture of `1^(@)` amides (benzenoid) having molecular formula `(C_(8)H_(9)NO)` reacted with `Br_(2)//NaOH`. The number of `1^(@)` amines products formed will be :

Explanation

To solve the problem, we need to determine how many primary amines can be formed from a mixture of primary amides with the molecular formula \( C_8H_9NO \) when they react with \( Br_2 \) in the presence of \( NaOH \).

### Step-by-Step Solution:

1. **Identify the Structure of Primary Amides**:
- The amide functional group is represented as \( C=O \) (carbonyl) attached to \( NH_2 \) (amine).
- Since the amides are benzenoid, they will have a benzene ring attached to the amide group.

2. **Determine Possible Structures for \( C_8H_9NO \)**:
- The molecular formula \( C_8H_9NO \) indicates that we have a benzene ring (which contributes \( C_6H_5 \)) and additional atoms to account for the remaining \( C_2H_4NO \).
- Possible structures for the amides can be:
- \( C_6H_5C(=O)NH_2 \) (Benzamide)
- \( C_6H_4(CH_3)C(=O)NH_2 \) (with \( CH_3 \) at ortho, meta, or para positions).

3. **Count Possible Isomers**:
- The methyl group \( CH_3 \) can be placed at three different positions on the benzene ring:
- Ortho position
- Meta position
- Para position
- Thus, we can have the following four primary amides:
1. \( C_6H_5C(=O)NH_2 \) (Benzamide)
2. \( C_6H_4(CH_3)C(=O)NH_2 \) (Ortho)
3. \( C_6H_4(CH_3)C(=O)NH_2 \) (Meta)
4. \( C_6H_4(CH_3)C(=O)NH_2 \) (Para)

4. **Reaction with Bromine and Sodium Hydroxide**:
- The reaction of primary amides with \( Br_2 \) in the presence of \( NaOH \) leads to the Hofmann degradation reaction, which converts the amide to a primary amine by removing the carbonyl group.
- The general reaction can be summarized as:
\[ R-C(=O)NH_2 \xrightarrow{Br_2/NaOH} R-NH_2 \]

5. **Identify the Products**:
- Each of the four amides will yield a corresponding primary amine:
1. From Benzamide: \( C_6H_5NH_2 \)
2. From Ortho-substituted amide: \( CH_3C_6H_4NH_2 \)
3. From Meta-substituted amide: \( CH_3C_6H_4NH_2 \)
4. From Para-substituted amide: \( CH_3C_6H_4NH_2 \)

6. **Count Unique Primary Amines**:
- The four amides yield four distinct primary amines:
1. \( C_6H_5NH_2 \) (Benzamine)
2. \( CH_3C_6H_4NH_2 \) (Ortho)
3. \( CH_3C_6H_4NH_2 \) (Meta)
4. \( CH_3C_6H_4NH_2 \) (Para)

7. **Conclusion**:
- The total number of unique primary amines formed is **4**.

### Final Answer:
The number of primary amines products formed will be **4**.