A minor sixth is the
chord you get when you take a
minor triad and add the sixth note of the
scale. They're notated
Cm6.
For example, an F minor triad is F Ab C. The sixth note of the F scale (major or minor) is D, so the Fm6 chord consists of F Ab C D.
Compare with the major sixth: the only difference is the underlying triad.
This chord is functionally similar to the
minor seventh, flat 5 (
m7b5) built on the
relative minor: the component notes are identical, but the
root note is of course different:
Gm6 = G Bb D E
Em7b5 = E G Bb D
The two can be interchanged with little bother for the sake of an effective bassline.