#"KClO"_3("s")" + heat"##rarr##"KCl(s)" + "O"_2("g")"#

Notice that the number of atoms of #"K"# and #"Cl"# are the same on both sides, but the numbers of #"O"# atoms are not. There are 3 #"O"# atoms on the the left side and 2 on the right. 3 and 2 are factors of 6, so add coefficients so that there are 6 #"O"# atoms on both sides.

#"2KClO"_3("s")" + heat"##rarr##"KCl(s)" + "3O"_2("g")"#

Now the #"K" and "Cl"# atoms are not balanced. There are 2 of each on the left and 1 of each on the right. Add a coefficient of 2 in front of #"KCl"#.

#"2KClO"_3("s")" + heat"##rarr##"2KCl(s)" + "3O"_2("g")"#

The equation is now balanced with 2 #"K"# atoms, 2 #"Cl"# atoms, and 6 #"O"# atoms on both sides.