Every fingering that fits a hand
x222
moderate · barre · no 5
767x
easy · no 5
7675
hard · no 5
7979
moderate · barre
7679
hard · no 5
What is true of it
D6 is D, F♯, A and B — 1, 3, 5 and 6 counted from D.
These are also the notes of Bm7/D. 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 x222: one finger, one of them barring the 2nd fret, 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.
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.
1 string stays silent.
Where its notes are on the neck
The brass dots are D, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
D6/F♯
x675
D6/A
2222
D6/B
4220
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.