Look at each molecule (or ion, like CO3) individually and see if it either A) changes phase or B) remains in the same phase. By phase I mean that aq, g, liq, or s.
In the specific case above, Barium and Chloride changed phase, while the other two remained the same. Since they remained the same, they can cancel each other out. When you then do the NIE, you have to also balance it. In this case, Barium is an alkaline-earth metal (it forms a +2 ion), therefore you need 2 Chlorides to balance out the equation.