These 2 remixes were the very first Ayu songs I've ever listened to (even before I listened to her regular songs), and I fell in love with them! So I'm nominating:
TO BE (Eurobeat Remix)
evolution "time is pop mix"
Also my very favorite of her remixes is the WE WISH remix for Ayu-trance 3, but it's already nominated so in that case I'll nominate my second favorite as well
Rule Remo-con "tech dance" remix