Balancing the reaction is done to obey the law of nature, particularly, the Law of Definite Proportions. The concept is, the amount of the same element before and after the reaction must be the same. This is actually a redox reaction.
Oxidation half-reaction: Zn + 4 OH⁻ → Zn(OH)₄²⁻ + 2 e-
Reduction half-reaction: NO₃⁻ + 6 H₂O + 8 e-→ NH₃ + 9 OH⁻
Adding both reaction, we get the overall complete balanced equation:
4Zn + NO₃⁻ + 6 H₂O + 7 OH⁻ → 4 Zn(OH)₄²⁻ + NH₃
Thus, the charge in the product side is 4*-2 = -8.
