The standard grips this chord is usually shown with.
Abm6 is Ab, Cb, Eb and F, a minor sixth. The shape this page opens on is written 4x3444, lowest string first.

Also written Abmin6, Ab-6 or Ab minor 6. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 8 common shapes for Abm6 on the guitar, and 28 derived voicings in 3 families.
In which keys. Every note of Abm6 belongs to Eb minor (the iv) and F# major (the ii).
The common shapes, written lowest string first: 4x3444, x2314x, 466464, xx6867, x-11-9-10-9-11, x-11-13-10-12-x, x-11-13-x-12-13, x-x-13-13-12-13.
Shell. Root, third and seventh: the guide tones fix the quality, so the fifth is dropped. That is what leaves a string free, so pick a tension to put on top. Abm6 has 423xxx, x-11-9-10-x-x, 4x34xx, x-11-x-10-12-x, 489xxx.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Abm6 has xx1101, 1211xx, xx3444, x6646x, xx6867, 7868xx, x8989x, 11-11-9-10-x-x.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Abm6 has x2x141, 1x110x, 4x344x, x6x464, 7x686x, x8x897, 11-x-9-10-9-x, x-11-x-10-12-11.
Tensions. A shell of Abm6, root, third and seventh, leaves a string free, and the tones that belong over it are the 9 (Bb) and the 11 (Db).
The common shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.