Here's how to balance the chemical equation for the reaction of tetraphosphorus decoxide (P₄O₁₀) with water (H₂O) to produce phosphoric acid (H₃PO₄):

1. Write the unbalanced equation:

P₄O₁₀ + H₂O → H₃PO₄

2. Balance the phosphorus (P) atoms:

There are 4 phosphorus atoms on the left side (P₄O₁₀) and only 1 on the right side (H₃PO₄). To balance this, put a coefficient of 4 in front of H₃PO₄:

P₄O₁₀ + H₂O → 4H₃PO₄

3. Balance the oxygen (O) atoms:

Now there are 10 oxygen atoms on the left side (P₄O₁₀) and 16 on the right side (4 x 4 = 16 in 4H₃PO₄). To balance the oxygen, put a coefficient of 6 in front of H₂O:

P₄O₁₀ + 6H₂O → 4H₃PO₄

4. Balance the hydrogen (H) atoms:

There are 12 hydrogen atoms on the right side (4 x 3 = 12 in 4H₃PO₄) and 12 hydrogen atoms on the left side (6 x 2 = 12 in 6H₂O).

5. The balanced equation:

The balanced equation is:

P₄O₁₀ + 6H₂O → 4H₃PO₄