`CH_(4)` can be prepared by the reaction of `H_(2)O` with:

Options

A. (a) `Mg_(2)C_(3)`
B. (b) `CaC_(2)`
C. (c) `Be_(2)C`
D. (d) `A1_(4)C_(3)`

Explanation

To determine which carbide can react with water (H₂O) to produce methane (CH₄), we will analyze the reactions of different carbides with water.

### Step-by-Step Solution:

1. **Identify the Carbides**: We are given several carbides:
- Magnesium carbide (Mg₂C₃)
- Calcium carbide (CaC₂)
- Beryllium carbide (Be₂C)
- Aluminium carbide (Al₄C₃)

2. **Reactions with Water**:
- **Magnesium Carbide (Mg₂C₃)**:
\[ \text{Mg}_2\text{C}_3 + \text{H}_2\text{O} \rightarrow \text{CH}_3\text{C} \equiv \text{CH} + 2\text{Mg(OH)}_2 \]
- This reaction produces propyne (C₃H₄), not methane (CH₄). Thus, this is incorrect.

- **Calcium Carbide (CaC₂)**:
\[ \text{CaC}_2 + \text{H}_2\text{O} \rightarrow \text{C}_2\text{H}_2 + \text{Ca(OH)}_2 \]
- This reaction produces acetylene (C₂H₂), not methane (CH₄). Thus, this is incorrect.

- **Beryllium Carbide (Be₂C)**:
\[ \text{Be}_2\text{C} + 4\text{H}_2\text{O} \rightarrow \text{CH}_4 + 2\text{Be(OH)}_2 \]
- This reaction produces methane (CH₄). Thus, this is correct.

- **Aluminium Carbide (Al₄C₃)**:
\[ \text{Al}_4\text{C}_3 + 12\text{H}_2\text{O} \rightarrow 3\text{CH}_4 + 4\text{Al(OH)}_3 \]
- This reaction also produces methane (CH₄). Thus, this is correct.

3. **Conclusion**: The carbides that can react with water to produce methane (CH₄) are:
- Beryllium carbide (Be₂C)
- Aluminium carbide (Al₄C₃)

### Final Answer:
The correct options are **Beryllium carbide (Be₂C)** and **Aluminium carbide (Al₄C₃)**.

---