The question provides us a precipitation reaction (shown below) and asks us which compound would not form ions considering the complete ionic reaction.
The reaction provided by the question is:
Pb(NO3)2(aq) + 2KI(aq) → PbI2(s) + 2KNO3(aq)
where lead nitrate (Pb(NO3)2) reacts with potassium iodide (KI) to produce the solid lead iodide (PbI2) and the sald potassium nitrate (KNO3)
To answer this question, we need to keep in mind that in a complete ionic reaction, soluble ionic compounds and strong acids are rewritten as dissociated ions. This does not include ionic compounds that aren't soluble in the considered system, such as the solid that is obtained in the reaction given.
Considering that information, the compound that would not be represented as dissociated ions is PbI2, because it is the solid obtained in the precipitation reaction (it is not soluble in the conditions of the reaction)