The major sixth chord is built upon the major chord by adding the sixth note of the major scale.
i.e., Major chord formula: 1 3 5
Major sixth chord formula: 1 3 5 6
e.g., The G6 chord is based upon the notes of the G major scale.
G Major Scale
Here is a common movable shape for the sixth chord shown at the third fret i.e., G6. This is a root 6 shape.
G6 (Root 6)