First, we need to find the chemical equation:
[tex]2KI+Pb(NO_3)_2\to PbI_2+2KNO_3[/tex]We can identify that the reactants gives a precipitation reaction which mean that there's a product that doesn't dissolve in water.
The net ionic equation shows only the chemical species involved in the reaction.
You can see it by separating the elements of a compound, like this:
[tex]2K^++2I^-+Pb^{2+}+2N^{}O^{2-}_{^{}3^{}}\to PbI_2+2K^++2NO^{2-}_3^{}[/tex]The NO3 looks the same because it doesn't suffer any change during the reaction, while the other reactants do.