The minor sixth chord is created by adding the sixth note of the major scale to the minor chord.
i.e., Minor chord formula: 1 b3 5
Minor sixth formula: 1 b3 5 6
e.g., The Gm6 is based upon the notes of the G major scale.
G Major Scale
Here is a common movable shape for the m6 chord shown here at the third fret e.g., Gm6. This is a root 6 shape.
Gm6 (Root 6)
The 5th string is deadened by the second finger.