Fill in the coefficients that will balance the following reaction: a0ki + a1pb(no3)2 → a2pbi2 + a3kno3

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