If it is just a simple double-replacement reaction, then the balanced equation is simply:
Pb(ClO3)2(aq) + 2 NaI(aq) = PbI2 + 2 Na(ClO3)
However, if this is a precipitation reaction, we must identify which compound will precipitate (is insoluble), either NaClO3 or PbI2
NaClO3 is soluble, PbI2 is not. Only the lead cations and iodine anions will participate in the reaction.
thus, the balanced equation is: Pb^(2+) + 2I^(-) ==> PbI2