Scales to Play Over F#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 F#m6 chord contains the notes F# – A – C# – D#. Any scale that includes every one of those 4 tones fits over it — from the root F#, that means F# Melodic Minor, F# Rock 'n' Roll, F# Dorian, F# Dorian Bebop, F# Half Whole Diminished and F# Gypsy Major. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
F#m6 is also diatonic to one major key: E major (relative minor C#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.