Every fingering that fits a hand
0201
open
0401
easy · no 5
0465
easy
0431
easy · no 5
046x
easy · no 5
What is true of it
Gm6 is G, B♭, D and E — 1, b3, 5 and 6 counted from G.
These are also the notes of Em7♭5/G. 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 0201: 2 fingers, held at the 1st fret.
1 of them use open strings, which is what makes a shape quiet to change to.
Where its notes are on the neck
The brass dots are G, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
Gm6/B♭
3435
Gm6/D
7767
Gm6/E
9aaa
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.