Total number of the following ethers that can be prepared by Williamson synthesis is `:`
`C_(6)H_(5)CH_(2)OC_(6)H_(5),C_(6)H_(5)OC_(6)H_(5),(CH_(3))_(3)COCH_(2)CH_(3),(CH_(3))_(3)COC(CH_(3))_(3),C_(6)H_(5)OCH_(2)CH_(3),CH_(3)OCH_(2)CH_(3)`

Explanation

To determine the total number of ethers that can be prepared by Williamson synthesis from the given compounds, we need to analyze each ether and see if it can be synthesized using the Williamson synthesis method. The Williamson synthesis involves the reaction of an alkoxide ion (RO⁻) with a primary alkyl halide (R'X). The key point is that the alkyl halide must be a primary halide for the reaction to proceed successfully.

### Step-by-Step Solution:

1. **C₆H₅CH₂OC₆H₅ (Diphenyl ether)**:
- This ether can be synthesized by using C₆H₅CH₂X (where X is a halogen) as the alkyl halide and C₆H₅O⁻ as the nucleophile.
- Since C₆H₅CH₂X is a primary alkyl halide, this ether can be prepared.
- **Possible**.

2. **C₆H₅OC₆H₅ (Phenyl ether)**:
- This ether involves the use of C₆H₅O⁻ and C₆H₅X. However, the C₆H₅X bond has partial double bond character, making it difficult for the nucleophile to attack.
- **Not possible**.

3. **(CH₃)₃COCH₂CH₃ (Tert-butyl ethyl ether)**:
- The alkyl halide would be CH₃CH₂X (a primary alkyl halide) and the nucleophile would be (CH₃)₃CO⁻.
- Since CH₃CH₂X is a primary alkyl halide, this ether can be prepared.
- **Possible**.

4. **(CH₃)₃COC(CH₃)₃ (Tert-butyl tert-butyl ether)**:
- This ether would require a tertiary alkyl halide (C(CH₃)₃X), which is not suitable for Williamson synthesis as it leads to elimination rather than substitution.
- **Not possible**.

5. **C₆H₅OCH₂CH₃ (Phenethyl ether)**:
- Here, we can use C₆H₅O⁻ as the nucleophile and CH₃CH₂X (a primary alkyl halide) as the alkyl halide.
- Since CH₂CH₃X is a primary alkyl halide, this ether can be prepared.
- **Possible**.

6. **CH₃OCH₂CH₃ (Ethyl methyl ether)**:
- In this case, CH₃O⁻ can react with CH₃CH₂X (a primary alkyl halide).
- Since CH₂CH₃X is a primary alkyl halide, this ether can be prepared.
- **Possible**.

### Summary of Analysis:
- Possible ethers from Williamson synthesis:
1. C₆H₅CH₂OC₆H₅
2. (CH₃)₃COCH₂CH₃
3. C₆H₅OCH₂CH₃
4. CH₃OCH₂CH₃

- Total possible ethers = 4.

### Final Answer:
The total number of ethers that can be prepared by Williamson synthesis is **4**.