This piece opens up with a D6/F# on the top three strings. This is a great Maj6th shape; we've covered a number of Maj6th shapes in this course, and it's good to collect as many Maj6th inversions as you can all over the fretboard as they really conjure that swing feel.
In the 4th measure, we walk this shape down two frets to a D9/E. This descending move into a 9th chord is one you can apply to most Maj6th fingerings, and a key sound to experiment with. Over the IV chord we grab a G7/D, then drop our first finger down a half-step to form a G6/D for the 2nd measure of the IV. This leaves us right in position for a sliding D9 - D13 move on the 5th to 7th frets.
For the turnaround, we take an A9/G and slide that up to an A6. The turnaround uses the same basic chords that we used over the I chord, but on a different set of strings and moving in the opposite direction. Then for the final turnaround, we have a great voicing leading passage that begins with a D9/C (the "Freddie King Hideaway Chord").