Ptolemy's model of the solar system explained the apparent changes in speed and direction of the planets primarily through the concept of epicycles. In his geocentric model, Ptolemy proposed that each planet moved in a small circle called an epicycle, which in turn moved along a larger circle called a deferent, centered around the Earth. This combination of motions allowed for the observed variations in a planet's speed and direction, including retrograde motion, where a planet appears to move backward relative to the stars.
Therefore, among the given options, the correct explanation for how Ptolemy's model accounted for the changes in speed and direction of the planets is:
The planets spun on epicycles.