Let a, b, c be the coefficients in the balanced reaction,
a P₄O₁₀ + b H₂O ⇒ c H₃PO₄
Count the number of each atom on either side of the reaction:
• P : 4a = c
• O : 10a + b = 4c
• H : 2b = 3c
Suppose a = 1. Then from the first equation,
c = 4•1 ⇒ c = 4
and from the third equation,
2b = 3•4 = 12 ⇒ b = 6
The third equation is also satisfied:
10a + b = 4c ⇒ 10•1 + 6 = 4•4 ⇒ 16 = 16
So, the balanced reaction is
P₄O₁₀ + 6 H₂O ⇒ 4 H₃PO₄
which makes D the correct answer.