Gailileo had studied perspective, exercises which involved the art of seeing and representing things from different viewpoints.
    He creatively inverted the method of calculating heights by using shadows, by using light instead.
    He mentally rotated the picture of the moon he saw through the telescope, to view the moon from another [imagined] viewpoint.
    He realized that he could apply what he knew, the Pythagorean theorem, to the problem of finding out how tall the mountains were.
    He made approximations, without worrying too much about how precise and accurate they were [it turns out that the calculation is relatively insenstive - it doesn't change very much- to different approxmations.  That is, a small "error" in input makes no practical difference to the output.]
    He showed that lunar mountains had to be very much like terrrestrial mountains, in terms of their heights.
 

The most important feature of this whole creative process was that Galileo used his imagination.

He created a world in his mind, labelled it with characteristics idealized from experience, manipulated that imaginary world, and discovered new characteristics which he could logically and rationally defend in the world of our experience.