The process of balancing chemical equations involves putting coefficients on reactants and products to ensure the number of atoms of each element is equal on both sides of the equation.
It is a try and error method that is done to make an equation obey the law of conservation of mass.
In this case;
Our unbalanced equation is, AgI + Fe₂(CO₃)3 → FeI₃+ Ag₂CO₃
It can be balanced by putting the coefficients 6, 1, 2, 3.