C6, restacked
The high-G C6 keeps C6's four notes, C, E, G and A, and restacks them: E G A C E G from the low string up, with a G on string 1 where C6 has its high E. Struck open it still rings as C6 or Am7, and a bar or a slant spells the same eight chord types as C6.
What changes is where the chords sit. With G, E and C on the top three strings, a C major triad lies across strings 1 to 3, where C6 has E, C and A, an A minor triad.
The retune
Every string moves, by two to four semitones. String 1 goes up three, from E to G, and the low string up four, from C to E.
Which high-G C6
The name covers more than one row. On eight strings it is often written with extra low strings; this page publishes the six-string row two independent sources print, E G A C E G.