Play A6/9 one string at a time and you hear A, C#, E, F# and B. A is the root, C# the major third, E the fifth, F# the sixth and B the ninth. Said aloud, its notes are A, C sharp, E, F sharp and B.
From the low string to the high one you hear A, F#, B, C# and E. The lowest note is A on string 5 and the highest is E on string 1.
A6/9 lets two strings ring open. String 5 gives A and string 1 gives E. String 6 is not played. Everything fits between frets 2 and 4. The second shape on this page starts at fret 4.
Aadd9 is one change away. String 4 moves from fret 4 to fret 2, bringing in E, the fifth of Aadd9. A6/9 holds the whole F#m chord inside it, A, C# and F#. Going to Bm, two positions stay the same.
A6/9 shows up in six keys. In A major it is the I6/9, in D major the V6/9 and in E major the IV6/9. The rest appear in the key list.