Could you explain how to derive the PPF for the question below?

1. Robinson Crusoe can produce two goods, X and Y, using the following production technologies: X 5 Lx and Y 6LY . His preferences over the two goods can be expressed by his utility function U (X, Y) = X Y2 and he is only willing to work a total of 6 hours in a day. a. [4] Derive the equation of his production possibilities frontier (express the quantity of good Y as a function of good X).