Suppose that x, y, z are positive integers satisfying \(x \le y \le z \), and such that the product of all three numbers is twice their sum. What is the sum of all possible values of z?

I don't understand your LaTex, but here are a couple of numbers that satisfy your question;

x = 1, y= 3, z = 8 and

x = 1, y = 4, z =5

Thanks. The latex is x is less than or equal to y which is less than or equal to z