Sixths (and thirds) are very important intervals in the major/minor system.
I can immediately think of two reasons:
- If the tonic chord is played (example
C major) and we played the chord without a sixth/third, we would only have the tones
G and we could not hear if the chord is major or minor. So the major/minor quality of harmony comes from the sixths/thirds and that is essential for major/minor system harmony.
- Secondly, in terms of voice leading consecutive sixths/thirds are acceptable and frequently encountered. By contrast, according to the traditional voice leading of Sor's time, you should not use move than one fifth consecutively. So the constraints of good voice leading lead to a propensity of sixths/thirds.
Given the harmonic importance of sixths/thirds, you want to be perfectly fluent in playing them in any key, any position within the scale, and with variety of connecting motions. Notice that the exercise has a few chromatic notes to highlight the
F chords. Those chromatic moves using sixths/thirds should also become perfectly familiar.
An exercise of only sixths packs all that important harmonic material into a very short space.
In terms of physical technique this exercise isn't very difficult. It doesn't involve rapid movements, or long stretches, etc. For this reason the main focus of the exercise seem to be about harmony. In terms of physical technique, I imagine main thing is to become aware of the different sequences of major and minor sixths in the scale and execute them with good fingering. I think, speed isn't the goal but rather an relaxed, automatic movement.
I play exercises like this on piano, and I play them in every key. You could try transposing it to other keys. Also, all these sixths are broken sixths, but you could try play the two notes of the sixths simultaneously. Just a suggestion. Simple exercises like this seem to invite modification after you can play them without any trouble.