OK. Let's take the Am6 arpeggio - which is what I show in the lesson.
It works over Am6 (obviously)
It works over C Major (with the caveat that it has an F# - which is a #11 or b5. So keep in mind the F# will sound "out" unless you have a Major chord with a b5 or #11. Definitely has a Lydian sound. Sometimes it's nice to play it over a straight Maj7 chord and resolve your F# note to a G. Tension/release)
It works over D9. (Basically it's a D9 without the root)
It works over a F#m7b5. (Same exact notes - different roots)
And lastly it works over any Ab Dominant altered chord. (Ab7b5, Ab7b5b9, etc. Uber-jazzy sound)
The tricky thing here is how to connect the dots and find the right min6 arpeggio for the chord you're playing. In other words - you don't want to think, "What can I play an Am6 arpeggio over?" You want to think from the chord you're playing, e.g. What min6 arpeggio works over a D9? ALWAYS work from the chord.
So let's reverse engineer this.
So for a Major chord - think relative minor. (The relative minor - or 6th - of C is A)
For a Dom7 or 9 chord, think the 5th of the chord. (The 5th of a D9 is A)
For a min7b5 chord, think the 3rd of the chord. (the 3rd of a F#m7b5 is A)
For an Ab Alt chord think 1/2 step up. (A half step up from the root of a Ab7b5#9 is A)
Hope that makes sense!
Cheers!
PG