The first step is to balance the number of oxygen atoms in the equation.
In the reactants, there are 3 atoms of oxygen, in the products, there is only one atom. To balance it, we have to assign 3 as the coefficient of K2O.
[tex]K+B_2O_3\to3K_2O+B[/tex]Now, we have to balance potassium, there is one atom of potassium in the reactants and 6 of them in the products. Assign 6 as the coefficient of K:
[tex]6K+B_2O_3\to3K_2O+B[/tex]Finally, balance boron. There are two atoms of boron in the reactants and only one of them in the product. Assign 2 as the coefficient of B:
[tex]6K+B_2O_3\to3K_2O+2B[/tex]And that is the balanced equation.