Calgon is `Na_2[Na_4(PO_4)_3)]`,

Explanation

To determine whether the statement "Calgon is `Na_2[Na_4(PO_4)_3]`" is true or false, we will analyze the composition and properties of Calgon.

### Step-by-Step Solution:

1. **Identify Calgon**:
- Calgon is commonly known as sodium hexametaphosphate. Its chemical formula is often represented as `Na6P6O18`.

2. **Understanding Hard Water**:
- Hard water contains soluble salts, primarily calcium (Ca²⁺) and magnesium (Mg²⁺) ions. These ions contribute to the hardness of water.

3. **Function of Calgon**:
- Calgon is used to remove permanent hardness from water. It does this by forming complexes with the calcium and magnesium ions present in hard water.

4. **Reaction with Hard Water**:
- When Calgon is added to hard water, it dissociates to release sodium ions (Na⁺) and forms a complex with the calcium and magnesium ions. The reaction can be simplified as:
- `Na6P6O18 + Ca²⁺/Mg²⁺ → Na2CaP6O18 + Na2MgP6O18`
- This complex keeps the calcium and magnesium ions in solution, effectively removing the hardness.

5. **Analyzing the Given Formula**:
- The provided formula `Na2[Na4(PO4)3]` suggests a different composition than what is known for Calgon.
- The correct formula for Calgon is `Na6P6O18`, which does not match the provided formula.

6. **Conclusion**:
- Since the formula `Na2[Na4(PO4)3]` does not accurately represent Calgon, the statement is **FALSE**.