Every fingering that fits a hand
x213
easy · no 5
7988
hard
7585
hard · no 5
7588
hard · no 5
758x
easy · no 5
What is true of it
Dm7 is D, F, A and C — 1, b3, 5 and b7 counted from D.
These are also the notes of F6/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 x213: 3 fingers, held at the 1st 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.
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
Dm7/F
acac
Dm7/A
2213
Dm7/C
5555
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.