Step 1 - Understanding the reaction
This reaction is a precipitation reaction: one of the products formed by the reaction is water-insoluble. This is also called, for simplicity sake, a douple-replacement reaction.
In such reactions, the cations will exchange their places, i.e., they will combine with the other cation's anion:
[tex]AB+CD\to AD+BC[/tex]Step 2 - Solving the equation
Note Ba(2+) ion is ionic-bonded to Cl(-) anion, whereas K(+) ion is bonded to CO3(2-) anion. They will exchange places:
[tex]\text{BaCl}_{2(aq)}+K_2CO_{3(aq)}\to\text{KCl}_{(aq)}+Ba_{}CO_{3(s)}[/tex]Note BaCO3 is a solid compound, because it is not soluble in water.
Step 3 - Balancing the reaction
To properly balance this reaction we have to multiply KCl by two:
[tex]\text{BaCl}_{2(aq)}+K_2CO_{3(aq)}\to2\text{KCl}_{(aq)}+Ba_{}CO_{3(s)}[/tex]