The number of hyperconjugating structures shown by the carbocations are given below. Which one is not correctly matched?

Options

A. `CH_(3)-underset(CH_(3))underset("| ")overset(+)"C "-CH_(3)`, 9 hyperconjugating
B. `CH_(3)-overset(+)C-CH_(3)`, 8 hyperconjugating structures
C. `CH_(3)-overset(+)CH_(2)`, 3 hyperconjugating structures
D. `overset(+)CH_(3)`, No hyperconjugating structures

Answer

To solve the question regarding the number of hyperconjugating structures shown by the carbocations, we will analyze each option provided and determine which one is incorrectly matched.

### Step-by-Step Solution:

1. **Understanding Hyperconjugation**:
- Hyperconjugation is the interaction between the electrons in a σ-bond (usually C-H or C-C) and an adjacent empty or partially filled p-orbital. This interaction stabilizes the carbocation.

2. **Identifying Carbocations**:
- We need to identify the carbocations in each option and count the number of hyperconjugating structures they can exhibit.

3. **Counting Hyperconjugating Structures**:
- For each carbocation, we will count the number of adjacent carbon atoms that can donate σ-bonds to the empty p-orbital of the carbocation.

4. **Analyzing Each Option**:
- **Option 1**: If the carbocation has 3 adjacent carbons, the number of hyperconjugating structures is 3 (from each adjacent carbon) × 3 (the number of hydrogens on each adjacent carbon) = 9.
- **Option 2**: If the carbocation has 2 adjacent carbons, the number of hyperconjugating structures is 2 × 3 = 6. (This option is incorrectly matched if it states 8).
- **Option 3**: If the carbocation has 1 adjacent carbon, the number of hyperconjugating structures is 1 × 3 = 3.
- **Option 4**: If the carbocation has 3 adjacent carbons again, the number of hyperconjugating structures is 3 × 3 = 9.

5. **Conclusion**:
- After analyzing all options, we find that **Option 2** is the one that is not correctly matched, as it states 8 instead of the correct 6 hyperconjugating structures.

### Final Answer:
The option that is not correctly matched is **Option 2**.