A sixth chord is any triad with an added sixth above the root. For example, a major sixth chord built on C (denoted by C6, or CM6) consists of the notes C, E, G, and the added major sixth. Here are the 5 shapes for the sixth chord found in the open position. Other sixth chords (such as F6 and B6) can only be played by using a barred form of one of these 5 shapes.
C6G6D6 | A6E6 |