The notes of E6/9 are E, G#, B, C# and F#. E is the root, G# the major third, B the fifth, C# the sixth and F# the ninth. Said aloud, its notes are E, G sharp, B, C sharp and F sharp.
From the low string to the high one you hear E, B, E, G#, C# and F#. The root, E, shows up twice in the main shape. The lowest note is E on string 6 and the highest is F# on string 1.
In E6/9, string 6 is played open and adds E. Everything fits between frets 1 and 2. The second shape on this page starts at fret 6.
Eadd9 is one change away. String 2 is left open, bringing in B, the fifth of Eadd9. E6/9 holds the whole C#m chord inside it, E, G# and C#. The change that keeps the most fingers still is to E. Three stay in place.
You will find E6/9 in six different keys. In E major it is the I6/9, in A major the V6/9 and in B major the IV6/9. The rest appear in the key list.