Answer
$4PH_3(g) + 8O_2(g)\rightarrow 6H_2O(g)+P_4O_{10}(s)$
Work Step by Step
Phosphine is PH_3(g). Oxygen gas is $O_2(g)$. Water vapor is $H_2O(g)$. Tetraphosphorous decaoxide is $Ph_4O_{10}(s)$.
$PH_3(g) + O_2(g)\rightarrow H_2O(g)+P_4O_{10}(s)$
Add a coefficient of 4 to $PH_3$ to balance $P$.
$4PH_3(g) + O_2(g)\rightarrow H_2O(g)+P_4O_{10}(s)$
Add a coefficient of 6 to $H_2O$ to balance $H$.
$4PH_3(g) + O_2(g)\rightarrow 6H_2O(g)+P_4O_{10}(s)$
Add a coefficient of 8 to $O_2$ to balance $O$.
$4PH_3(g) + 8O_2(g)\rightarrow 6H_2O(g)+P_4O_{10}(s)$
