Which of the following values of u makes u(2 + u) – 2u = 16 true?

U(2+u) - 2u = 16
Whenever a problem presents itself with the words "what value of this variable makes this true", this means that it wants you to solve for the variable. It's the completely the same as "Solve." Now that we understand what the question is asking, we can solve for u.

u(2 + u) - 2u = 16
Distributive Property
2u +  - 2u = 16
Combine like terms
= 16
Subtraction of Equality
( - 16) = 0
Difference of Squares
(u - 4)(u + 4) = 0
u = 4, (-4)
Since you did not provide the choices, if any of the choices are (4) or (-4), then those choices are correct. Hope this helps!