Sorry but I can't understand what you want to know exactly.
The chemical equation I wrote describes the reaction taking place in an argentometric titration such as that used for determining the concentration of a sodium chloride sample.
If you want to investigate whether a reaction can occur, I think thermodynamics to be the answer.
However, I don't think you need it. The problems already shows you all the compounds involved: what other chemical equation could you predict, just reading the text of the problem?