Reactions are balanced by equating the right and the left side by stoichiometry coefficients. The redox reactions are balanced and corrected by simplifying the numbers.
A redox reaction is a depiction of the oxidation and the reduction of the reaction that shows the loss and the gain of the electrons by the chemical species.
The oxidation half-reaction:
Mg → Mg²⁺ + 2e⁻
The reduction half-reaction:
2Au + 2 e⁻ → 2 Au
The overall balanced reaction is:
Mg(s) + 2Au⁺ (aq) → Mg²⁺ (aq) + 2Au(s)
Therefore, the reaction is balanced by the oxidation and the reduction halves.
Learn more about redox equations here:
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