4NaCl + 2SO2 + _____H2O + _____O2 → _____Na2SO4 + 4HCl

To balance the given chemical equation:

4NaCl + 2SO2 + _____ H2O + _____ O2 → _____ Na2SO4 + 4HCl

First, we will determine the products and the number of each compound needed to balance it.

We need to identify the coefficients such that the number of atoms of each element on the left side equals the number of atoms of that element on the right side.

1. **Identify the products**:
- Sodium (Na) from NaCl will form Na2SO4.
- Sulfur (S) from SO2 will also be found in Na2SO4.
- Chlorine (Cl) from NaCl will form HCl.
- Water (H2O) will contribute hydrogens (H) to form HCl.
- Oxygen within SO2 and O2 contributes to the formation of Na2SO4.

2. **Count each atom**:
- On the left:
- Na: 4 (from 4NaCl)
- Cl: 4 (from 4NaCl)
- S: 2 (from 2SO2)
- O: 4 (from 2SO2)
- H: 0

- On the right:
- Na: 2 (from Na2SO4)
- Cl: 4 (from 4HCl)
- S: 1 (from Na2SO4)
- O: 4 (2 from Na2SO4 + O2)
- H: 4 (from 4HCl)

3. **Balancing the equation**:
- To balance sodium and sulfur, you need 2 Na2SO4 for 4 Na.
- For sulfur, 2SO2 provides enough sulfur for 2 Na2SO4.
- To balance chlorine and hydrogen, we need 4 H2O.

So, the balanced coefficients appear as follows:

4NaCl + 2SO2 + 4H2O + 0O2 → 2Na2SO4 + 4HCl

Thus, the balanced equation is:

**4NaCl + 2SO2 + 4H2O → 2Na2SO4 + 4HCl**