Yes, x is the distance from the center of the sphere to the center of the circular base of the cone. Having the background not so dark would have made it easier to read. Was this originally done on yellow paper?
Since the distance from the vertex of the cone is h and the distance from the vertex of the cone to the center of the sphere is 4, x= distance from center of sphere to center of the base of the cone is ?? As Avodyne said, you have a right triangle with hypotenuse 4, one leg equal to x and the other leg equal to the radius of the base.
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