6th Chords

To make a 6th chord, start with the triad and add the 6th. But note that the major 6th is added to make both major and minor 6th chords - the 'minor' or 'major' bit comes from the triads.

So - for a C6 chord:

Start with a C major triad (CEG) and add the major 6th (A).
C6 = C E G A

For a Cm6, start with a C minor triad (CEbG) and add the major 6th (A).
Cm6 = C Eb G A

6/9 chords

These are similar to 6th chords, but they have a 9th added, as you may have guessed! I've always seen this as major chords, but I guess there's no reason why you couldn't have something like Dm6/9.

Anyway they are built up by taking the basic triad, and adding the 6th and the 9th.

So C6/9 would be: 1st, maj 3rd, 5th, 6th, 9th

i.e. the notes are: C E G A D
(The 5th can sometimes be left out)

A nice shape for this C6/9 would be:

EADGBE
x32233

C 6/9