the answer
the main rule
A ----- B
A is the reactants and B the products of a reaction
the number of atome of the elements of A must be equal to the number of atome of the elements of B
in our case
to balance the equation
a0 KI + a1 Pb(NO3)2 → a2 PbI2 + a3 KNO3
2KI + Pb(NO3)2 → PbI2 + 2KNO3
proof
A (reactants ) -------------------- B (products)
2KI means 2K, 2I PbI2 : 2I, 2KNO3: 2K ( K and I are balanced)
Pb(NO3)2:
1 Pb, 2 NO3 PbI2 and 2KNO3:
1Pb and 2 NO3 (Pb and NO3 are balanced)
finally
a0= 2, a1= 1, a2= 1, a3=2