Every fingering that fits a hand
101x
open · no 5
1013
open · no 5
1313
moderate · barre
x888
moderate · barre · no 5
What is true of it
A♭6 is A♭, C, E♭ and F — 1, 3, 5 and 6 counted from A♭.
These are also the notes of Fm7/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 4 fingerings below is 101x: 2 fingers, held at the 1st fret.
2 of them use open strings, which is what makes a shape quiet to change to.
2 of the 4 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.
1 string stays silent.
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
A♭6/C
5546
A♭6/E♭
8888
A♭6/F
x543
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.