A windsurf duck gybe -- when the back hand is released (maybe 60 to 75 degrees off the wind [90 degrees is dead downwind] depending on wind strength) and replaced with what was the front hand the sail goes over the head (the duck) to the other side as the board is carved around the sail's mast. The sail's boom is now be grabbed by what was the back hand (now the front hand) on the other side and you switch your feet and sail away. With the wind foiling duck gybe the front hand is released and it replaces the back hand in the strap or on the boom (Echo) as you head well off the wind -- you pull the wing back a little with the back hand to help you position the wing so you can quickly grab it with the new front hand. The wind wing upon release of the back hand swings around in front of you while you carve (follow it) through the turn and what was your back hand (now your front hand) grabs a forward strap or the forward part of the boom (Echo) and you pick up power as you finish the carve and exit the gybe -- you might have to give the board and wing a couple of pumps to stay on foil if the wind is light. You can now switch your feet (if you didn't do this before entering the gybe) or not and foil away.
At the 4:30 mark in the attached video Balz Muller shows and explains how to do the duck gybe.