Every fingering that fits a hand
4242
hard · no 5
4645
moderate · barre
424x
easy · no 5
4245
hard · no 5
xbab
easy · no 5
What is true of it
Bm6 is B, D, F♯ and G♯ — 1, b3, 5 and 6 counted from B.
These are also the notes of G♯m7♭5/B and A♭m7♭5/B. 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 4242: 4 fingers, held at the 2nd fret.
None of them uses an open string, so this chord moves up the neck unchanged — the same shape 1 fret higher is the chord a semitone above.
1 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 B, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
Bm6/D
x242
Bm6/F♯
bbab
Bm6/G♯
1222
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.