Ba(ClO3)2 --> BaCl2 + 3 O2
The fact that there are some ionic compounds doesn't matter. Just use the formulas.
barium chlorate = Ba(ClO3)2
barium chloride = BaCl2
Oxygen = O2
Now create the unbalanced equation
Ba(ClO3)2 --> BaCl2 + O2
And balance in the usual fashion. Count the atoms of each element on both sides
Ba = 1, 1
Cl = 2, 2
O = 6, 2
And oxygen is out of balance. But can be easily handled with a 3 coefficient on the right hand side. So:
Ba(ClO3)2 --> BaCl2 + 3 O2
And we have a balanced equation.