To balance the reaction easily we can look at C2H3O2 like a polyatomic ion. This means that we balance it separately like its a single particle instead of breaking it down to its elements and balancing those elements individually.
In the reaction above, I've highlighted parts in blue and yellow. Ba here seems to be balanced for now so everything with Ba we leave alone (as in we don't change the coefficient for now).
Consider the unbalanced equation for the neutralization of acetic acid:
HC2H3O2(aq) + Ba(OH)2(aq) → H2O(l) + Ba(C2H3O2)2(aq)
Balance the equation.
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