Scales to Play Over Em6
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 Em6 chord contains the notes E – G – B – C#. Any scale that includes every one of those 4 tones fits over it — from the root E, that means E Melodic Minor, E Rock 'n' Roll, E Dorian, E Dorian Bebop, E Half Whole Diminished and E Gypsy Major. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
Em6 is also diatonic to one major key: D major (relative minor Bm). 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.