This one is a special case. It looks like the net rxn should be:
BaCO3 + 2HCl --> BaCl2 + H2CO3
But you're expected to know that H2CO3 (carbonic acid) spontaneously decomposes into H2O and CO2. So whenever it looks like H2CO3 should be the product, write H2O and CO2 instead. So the net ionic is:
BaCO3(s) + 2H+(aq) --> Ba2+(aq) + H2O(l) + CO2(g)
Cl- was eliminated as a spectator ion as it's part of a strong electrolyte on both sides of the rxn.
Again this really is a special case but one that you are expected to know.