First let's write down the chemical reaction.  This is an ion exchange reaction where we start with two substances (lead nitrate and potassium iodine) and get two new substances (lead iodine and potassium nitrate)

Pb(NO3)2 +KJ ->PbJ2 + KNO3

Next, we need to count the atoms on the right and on the left to see if they are in balance.

We can simplify the procedure by noting that NO3 does not change.

                                Left:                       Right:

Pb                           1                              1

NO3                       2                              1

K                             1                              1

J                              1                              2

NO3 and J are not in balance. We need to multiply by 2 KNO3 on the right and KJ on the left:

Pb(NO3)2 +2 KJ ->PbJ2 + 2 KNO3

Let us count the groups to see if additional balancing is needed to be done:

                                Left:                       Right:

Pb                           1                              1

NO3                       2                              2

K                             2                              2

J                              2                              2

Both parts are in balance!