A Major 6 chord is formed in a similar manner to the Major seventh chord. Instead of adding the seventh Major scale tone to a Major triad (which is how the Maj 7th chord is formed), we add the sixth scale tone from the Major scale. Consider a C Major scale. It has the notes C, D, E, F, G, A, B. The Major 6 chord contains the scale tones 1-3-5-6. So we end up with C-E-G-A.
Above are some of the most useful fingerings for Major 6 chords. In all cases I left out the 5th since it is not needed to capture the essence of the Major 6 sound.
Next time, I will show you useful fingerings for Minor 9th chords.