To balance the equation K + H2O → H2 + KOH, we need to make sure that the number of atoms of each element is the same on both sides of the equation.

Let's start with K. We have one K atom on the left side of the equation and one K atom on the right side, so that's balanced.

Now let's look at H. We have two H atoms on the left side of the equation and two H atoms on the right side, so that's also balanced.

Finally, let's look at O. We have one O atom on the left side of the equation and one O atom on the right side, so that's balanced as well.

Therefore, the equation is already balanced and does not need any coefficients to be added.