6th Chords, sometimes referred to as 6 Chords, are probably the most melancholy of all the chords (next to the Major 7th chord). Adding the 6th scale degree to the chord gives color without altering the scale or harmonic motion.
You are going to add the Major 6th scale degree on top of a major triad. If you have to play 6th chord quickly, just remember the 6th scale is always full step above the fifth of the chord.
Here's an easy 6th chord. Just take your regular 5th root power bar chord and simply extend the bar all the way through the high e string and that's the 6th of the chord. Viola!
Another way to think of 6th chords is to start with a familiar dominant 7th chord and just lower the b7 one more half-step and you have a 6th chord. This is a great way to find new shapes you never thought of.
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The following example is a practical finger. This chord is rooted on the low E string. This is very easy to finger quickly when you are reading charts. Notice you have redundancy with the root doubled. So you have a root-root-third-sixth structure going from high to low.
Once you've got down the shapes based on the low string, you want to build practical fingerings with roots on the A and D strings. Once you memorize the three main shapes, you will be able to hit the chord quickly when called for.