Scales to Play Over F#6/9
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.
An F#6/9 chord contains the notes F# – G# – A# – C# – D#. Any scale that includes every one of those 5 tones fits over it — from the root F#, that means F# Major, F# Major Pentatonic, F# Rock 'n' Roll, F# Lydian, F# Mixolydian, F# Dorian Bebop and F# Mixolydian Bebop. They differ only in the notes between the chord tones, and that is where each scale gets its color.
F#6/9 is also diatonic to 3 major keys: B major (relative minor G#m), Db major (relative minor Bbm), 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.