Scales to Play Over G#m6
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A G#m6 chord contains the notes G# – B – D# – F. Any scale that includes every one of those 4 tones fits over it — from the root G#, that means G# Melodic Minor, G# Rock 'n' Roll, G# Dorian, G# Dorian Bebop, G# Half Whole Diminished and G# Gypsy Major. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
G#m6 is also diatonic to one major key: F# major (relative minor D#m). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.