The 6th chord is a four-note chord that adds the sixth degree note in the scale to the major triad. By comparing C with C6 we could see that the notes changes from C, E, G to C, E, G, A.
6th chords in open positions
These are, generally, chords in open position, with F6 as an exception which is a closed chord (with no loose strings).
Noticeable is that B6 is played with an alternative bass note (F#), see different versions below.
The first chord diagram from the left is a popular way to play C6. It's easy to memorize since it has almost the same positions as C major. But it doesn't include a fifth (G). It's not strictly necessary to include the fifth, but alternative versions that do so are presented below.
Also noticeable is that F6 doesn't have a third (C). The presented version above is popular to play, but an alternative is mentioned below.
Chord constructionC6 E - A - E - G - C - G
D6 x - x - D - A - B - F#
E6 E - B - E - G# - C# - E
F6 x - x - F - A - D - F
G6 G - B - D - G - B - E
A6 x - A - E - A - C# - F#
B6 F# - B - D# - G# - B - x
Guitar versions of the chord
Notes in chordC6 C - E - G - A
D6 D - F# - A - B
E6 E - G#- B - C#
F6 F - A - C - D
G6 G - B - D - E
A6 A - C# - E - F#
B6 B - D# - F# - G#
The intervals are 1 – 3 – 5 – 6
The first C6 chord diagram is played with alternative bass note (E). It's possible to play without the 6th string also, making it a C6/A to be strict. The second diagram shows how C6 could be played by bar four strings on the fifth fret. This particular chord shape could be combined with a major 7th chord version with similar shapes. For example, Bb6/F (XX3333) and Bbmaj7 (XX3335).
The third diagram present a way to play F6 in open position and include all four tones belonging to it. However, it somewhat harder to play than the version presented above and not especially popular.
The diagram to the right presents a second way to play B6, this time with the root note on the bass string (5th string). It somewhat trickier than the open chord variation.
Movable 6th chord
Here are two ways to play the 6th with movable shapes, including a barre shape.
The root note is the same as the bass note in all examples.
Progressions including this chord type:
C6 - G11 - Dm7
A6 - B9 - Emaj7