Answer:
2Ba₃(PO₄)₂ +6SiO₂ ⇒ P₄O₁₀ +6BaSiO₃
Step-by-step explanation:
Equating coefficients, you get ...
aBa₃(PO₄)₂ +bSiO₂ ⇒ cP₄O₁₀ +dBaSiO₃
For Ba: 3a = d
For P: 2a = 4c
For O: 8a +2b = 10c +3d
For Si: b = d
__
Expressing everything in terms of b and c, we get ...
d = b
a = b/3 = 2c
From the second, b = 6c, so we have ...
a = 2c
b = 6c
c = c
d = 6c
And we can write the equation with c=1 as ...
2Ba₃(PO₄)₂ +6SiO₂ ⇒ P₄O₁₀ +6BaSiO₃