We can find the height by looking at what we know, and what we want to know.
We know that the volume of a rectangular prism can be found with the equation:
base width x base length x height = volume
We also know that the base's width x length = 10cm^2, so we can fill in what we know into the volume equation.
10cm^2 x height = 60cm^3
Solving this equation we find that the height if the prism is 6 cm.