Final answer:
When f(x) varies directly with x and f(x) = 24 for x = 2, the constant of variation is 12. To find f(x) for x = 6, multiply 12 by 6 to get f(x) = 72. Therefore the correct answer is Option D.
Step-by-step explanation:
The question asks about direct variation, which is a mathematical concept where one variable changes linearly with another. In this case, if f(x) varies directly with x, and f(x) = 24 when x = 2, the constant of variation k can be found by k = f(x)/x = 24/2 = 12. Therefore, the equation representing the relationship is f(x) = 12x. To find the value of f(x) when x = 6, substitute 6 into the equation: f(x) = 12 * 6 = 72. Hence, the correct answer is 72.