How many of the following ethers CANNOT be prepared by Williamson's synthesis?
`CH_(3)OCH_(2)CH_(3),C_(6)H_(5)OCH_(3), (C_(6)H_(5))_2O, (CH_(3))_(3)COCH_(3),(C_(2)H_(5))_2O, (CH_(3))_(3)C-O- C(CH_3)_(3)`

Answer

To determine how many of the given ethers cannot be prepared by Williamson's synthesis, we need to analyze each ether based on the principles of the synthesis.

### Step-by-Step Solution:

1. **Understanding Williamson's Synthesis**:
- Williamson's synthesis involves the reaction of an alkoxide ion (RO⁻) with an alkyl halide (R'X) to form an ether (ROR').
- The reaction proceeds via an SN2 mechanism, which is effective for primary alkyl halides and some secondary ones, but not for tertiary alkyl halides due to steric hindrance.

2. **List of Ethers**:
- **Ether 1**: CH₃OCH₂CH₃ (Ethyl methyl ether)
- **Ether 2**: C₆H₅OCH₃ (Methyl phenyl ether)
- **Ether 3**: (C₆H₅)₂O (Diphenyl ether)
- **Ether 4**: (CH₃)₃COCH₃ (Tert-butyl methyl ether)
- **Ether 5**: (C₂H₅)₂O (Diethyl ether)
- **Ether 6**: (CH₃)₃C-O-C(CH₃)₃ (Tert-butyl ether)

3. **Analyzing Each Ether**:
- **Ether 1 (CH₃OCH₂CH₃)**:
- Alkoxide: CH₃O⁻ (from CH₃OH)
- Alkyl halide: CH₃CH₂Cl (primary)
- **Possible via Williamson's synthesis**.

- **Ether 2 (C₆H₅OCH₃)**:
- Alkoxide: C₆H₅O⁻ (from C₆H₅OH)
- Alkyl halide: CH₃Cl (primary)
- **Possible via Williamson's synthesis**.

- **Ether 3 ((C₆H₅)₂O)**:
- Alkoxide: C₆H₅O⁻ (from C₆H₅OH)
- Alkyl halide: C₆H₅Cl (primary)
- **Possible via Williamson's synthesis**.

- **Ether 4 ((CH₃)₃COCH₃)**:
- Alkoxide: (CH₃)₃CO⁻ (from (CH₃)₃COH)
- Alkyl halide: CH₃Cl (primary)
- **Not possible due to steric hindrance (tertiary alkoxide)**.

- **Ether 5 ((C₂H₅)₂O)**:
- Alkoxide: C₂H₅O⁻ (from C₂H₅OH)
- Alkyl halide: C₂H₅Br (primary)
- **Possible via Williamson's synthesis**.

- **Ether 6 ((CH₃)₃C-O-C(CH₃)₃)**:
- Alkoxide: (CH₃)₃CO⁻ (from (CH₃)₃COH)
- Alkyl halide: (CH₃)₃CCl (tertiary)
- **Not possible due to steric hindrance (tertiary alkyl halide)**.

4. **Conclusion**:
- The ethers that cannot be prepared by Williamson's synthesis are:
- (CH₃)₃COCH₃ (Ether 4)
- (CH₃)₃C-O-C(CH₃)₃ (Ether 6)
- Therefore, **2 ethers cannot be prepared by Williamson's synthesis**.

### Final Answer:
**2 ethers cannot be prepared by Williamson's synthesis.**