Question

When the reaction shown is correctly balanced, the coefficients are: kclo3 → kcl + o2?

Answer 1

The balanced equation above will be;
2 KClO3 = 2 KCl +  3 O2 
Therefore, the coefficients are; 2,2,3
Which means 2 KClO3 will create 2 KCl and 3 oxygen molecules. 

Answer 2

From the balanced equation 2KClO3 → 2KCl + 3O2, the coefficients are the following:
coefficient 2 in front of potassium chlorate KClO3
coefficient 2 in front of potassium chloride KCl 
coefficient 3 in front of oxygen molecule O2

We got this balanced equation by identifying the number of atoms of each element that we have in the given equation KClO3 → KCl + O2.
Looking at the subscripts of each atom on the reactant side and on the product side, we have
     KClO3 → KCl + O2
       K=1          K=1
       Cl=1         Cl=1
       O=3          O=2

We can see that the oxygens are not balanced. We add a coefficient 2 to the 3 oxygen atoms on the left side and another coefficient 3 to the 2 oxygen 
atoms on the right side to balance the oxygens:
     2KClO3 → KCl + 3O2
The coefficient 2 in front of potassium chlorate KClO3 multiplied by the subscript 3 of the oxygen atoms on the left side indicates 6 oxygen atoms just as the coefficient 3 multiplied by the subscript 2 on the right side indicates 6 oxygen atoms.

The number of potassium K atoms and chloride Cl atoms have changed as well:
     2KClO3 → KCl + 3O2
       K=2            K=1
       Cl=2          Cl=1
       O=6           O=6

We now have two potassium K atoms and two chloride Cl atoms on the reactant side, so we add a coefficient 2 to the potassium chloride KCl on the product side: 
     2KClO3 → 2KCl + 3O2, which is our final balanced equation.
        K=2           K=2
        Cl=2          Cl=2
        O=6           O=6
The potassium, chlorine, and oxygen atoms are now balanced.