I think perhaps the OP's issue/question was not specifically about how to play an E6 chord, but about whether or not the keyboard's auto-accompaniment feature recognizes 6th chords. As most of you probably know, a style or auto accompaniment can consist of several parts-- on a Yamaha, they are typically Rhythm 1, Rhythm 2, Bass, Chord 1, Chord 2, Pad, Phrase 1, and Phrase 2-- and the chord that you play in the auto accompaniment zone determines the notes which will be played for most of these parts, so the question of whether or not the keyboard can recognize 6th chords is quite valid.
As I said, the keyboard does recognize 6th chords, and the owner's manuals for earlier models in the PSR-E4xx line did include a more complete list and diagram of the chords which are recognized, but for some reason Yamaha apparently decided to drop that information from the owner's manuals of later PSR-E4xx models, and this could very well lead owners to conclude that the more advanced chords are not recognized by the auto accompaniments.
Actually, the issue is a bit more complex than that, because Yamaha's SFF styles can be programmed such that only specific musical keys and/or types of chords will be recognized. Thus, even though the keyboard has the ability to recognize 6th chords, specific style files might be programmed to not recognize them as such and to respond to them as though they were some other type of chord. However, I suspect that most if not all of the built-in styles are programmed to recognize the full list of musical keys and chord types, given that they're intended to be flexible enough to be useful for playing a wide variety of compositions. But style files which were created for playing some specific song might conceivably be programmed to recognize a more narrow list of musical keys and chord types, presumably to make it easier for the performer to play the auto accompaniment correctly without having some unintended misfingering produce an undesired result.
