You calculate
-- the girl's forward momentum before she jumps
-- the girl's forward momentum after she jumps
-- the board's forward momentum while she's still on the board
Then you say "The forward momentum of girl+board has to be the same before and after the jump." and you find what the board's new momentum must be to make that true.
Finally, knowing the board's mass and new momentum, you can quickly crank out its nee speed and direction. (The board may take off backwards after the jump. That's OK.)