Here are some movable fingerings for major 6th chords, shown here as Bb6. These fingerings are all on groups of four adjacent strings - top four, middle four and bottom four.
The next group of shapes are also commonly used, and are not on groups of four adjacent strings. Each one relates to one of the five basic forms. As with all chord types, these are determined by the positions of the root notes.
Here is a guitar part using major 6th chords. The eighth notes in this example are swung, as indicated by the previous symbol. If you are not familiar with swing rhythms, see Complete Learn to Play Rhythm Guitar Manual.
A minor 6th chord is created by adding a 6th degree to any minor chord. For example, a Cm6 chord contains the notes C, Eb, G and A (1, b3, 5 and 6). The following diagram shows some common open minor 6th chord shapes.