G6/9 is built from G, B, D, E and A. G is the root, B the major third, D the fifth, E the sixth and A the ninth.
From the low string to the high one you hear G, B, D, A, B and E. The note heard most is B, twice. It is not the root but the major third. The lowest note is G on string 6 and the highest is E on string 1.
G6/9 lets three strings ring open. String 4 gives D, string 2 gives B and string 1 gives E. Everything fits between frets 2 and 3. The second shape on this page starts at fret 2.
Gadd9 is one change away. String 1 is pressed at fret 3, bringing in G, the root of Gadd9. G6/9 holds the whole Em chord inside it, G, B and E. The change that keeps the most fingers still is to G. Two stay in place.
G6/9 shows up in six keys. In G major it is the I6/9, in C major the V6/9 and in D major the IV6/9. The rest appear in the key list.