To balance a equation, we need to have the same number of atoms of each elements on both sides of the chemical reaction (reactant and product side).
I rewrote this substance(Zn(CH3COO)2) for better understanding.
__Zn + __HC2H3O2 → __Zn(C2H3O2)2 + __H2
Reactant side unbalanced:
Zn - 1
H - 4
C - 2
O - 2
Products side unbalanced:
Zn - 1
C - 4
H - 8
O - 4
Obs: when there is a part inside the parentheses, all the atoms are multiplied by the number outside the parentheses.
Now let's balance the equation changing the stoichiometric coefficient.
Zn + 2 HC2H3O2 → Zn(C2H3O2)2 + H2
Reactant side:
Zn - 1
H - 8
C - 4
O - 4
Product side:
Zn - 1
H - 8
C - 4
O - 4
Now the equation is balanced.
Answer: Zn + 2 HC2H3O2 → Zn(C2H3O2)2 + H2