Answer
$A_{2} + 4 BC_{2} → 4 C_{2} + 2 AB_{2}$
Work Step by Step
By observing the reaction, we note that in reactants:
A is of form $A_{2}$
B and C are of form $BC_{2}$
and the ratio of A:BC is 1:4
In products, we note:
A and B of the form $AB_{2}$
C of the form $C_{2}$
and the ratio of AB:C is 4:2