This exercise uses a new four chord progression: 1, 4, 7, 4. If you start on a C major triad (call this the 1), you would then need to go up a perfect fourth to find the next chord (the 4). In this case, a perfect fourth above C is F, so the second chord in the progression is F major. The third chord is based off a minor seventh above the root chord. Since Bb is a minor seventh above C, the third chord is Bb major. The second and fourth chords in the progression are the same, so you move back to F major for the final chord.
Once you have completed the cycle, move up a fourth from the last chord (in this case, back to Bb) and begin the cycle over again. You may also notice that each time you repeat the pattern you move down one whole step from where you started. In other words, since you started on C for the first cycle, you start on Bb (one whole step lower) for the second cycle, Ab for the third, and so on.
Once you have this progression mastered starting on C major, start on C# major and perform the same pattern. This will allow you to cover all the major chords.
Please always make music. Arpeggiate the chords or try different comps over the chords, but make sure you are comfortable with the concept of the exercise first. You should work on getting these sounds in your ears and hands so that when you hear something like this in your head you can express yourself and play it!