Every fingering that fits a hand
2120
open · no 5
212x
easy · no 5
2424
moderate · barre
x999
moderate · barre · no 5
2124
hard · no 5
What is true of it
A6 is A, C♯, E and F♯ — 1, 3, 5 and 6 counted from A.
These are also the notes of F♯m7/A and G♭m7/A. Which name is right depends on what is underneath and what came before — the notes alone do not decide.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is 2120: 3 fingers, held at the 1st fret.
1 of them use open strings, which is what makes a shape quiet to change to.
2 of the 5 need a barre.
It leaves out the 5. 4 strings cannot carry 4 notes, and the 5 is the one this chord can lose without changing what it is.
Where its notes are on the neck
The brass dots are A, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
A6/C♯
x120
A6/E
9999
A6/F♯
x654
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.