The highest possible score in yahtzee depends wildly on which variant of the game you are playing. Assuming that you are playing with the standard rules, then the highest best ever possible score in yahtzee would be to score a yahtzee on each turn with the appropriate number.
On the left, you would score: 5, 10, 15, 20, 25, 30 plus the 35 points bonus. The right hand side would be full of yahtzies on sixes, so you would have: 30, 30, 25, 30, 40, 50 and 30 and of course, 12 bonus yahtzees 1200. The total score therefore would be 140 from the left hand side plus 1435 from the right hand side, giving a grand total maximum possible best ever world record yahtzee score of 1575.