A 6th chord is a chord where  a major triad and the additional sixth interval is major (major sixth chord). 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 A . These are the same notes as those of an A minor seventh chord – whether such a chord should be regarded as an added sixth chord or a seventh depends on its context and harmonic function.

Fret/Chord Chart

You can determine the name of the chord when the root
(lowest) note is played on the frets in the chart below:

Alternate Fingering

Here is a poplular alternative way of playing the A style
6th barre chord. It’s the same form with the exception
of the missing note on the 5th string. It used a lot because
it’s an easer fingering than the full barre chord.