This is one of the coolest progressions to learn. Best of all, it flows very well and is fun to play.
There are three major patterns to study when playing this exercise. First, the chords alternate between major and minor with each chord change. This is helpful when first learning this exercise because you can listen for the change in the chord quality as you play each chord. If you don't hear the correct change, check to make sure you are playing the correct notes.
Secondly, the root note of each chord moves in a specific pattern; namely, down a minor third, then down a major third. If you start on C major (or any major chord, for that matter) and use this pattern you can cover every major and minor triad before you come back to C major (or the triad you started on).
Third, there is only a one note difference between any two adjacent chords in the entire exercise. This makes it very easy for your right hand to change each chord because you only need move one finger. For instance, when you change from C major to A minor, the G moves up to an A while the C and E remain. Then when you move to the F major chord, the E moves up to F while the C and A remain, and so on. Although it may appear that there is a different change when moving from Abm to E, this is only a result of respelling Fb major as an E major chord. The root movement is still down a major third and the Eb in the right hand moves to an E while the other notes stay the same.
Once you master this progression, begin on C major as usual, but instead of playing C, E, G in the right hand, use a different inversion; try playing E, G, C or G, C, E for example. If you can master this progression starting from all three inversions of C major, you will have covered every inversion of every major and minor triad.
Have fun with this. Stay loose. Take your time. Breathe.