Answer
$\dfrac{d^2y}{dx^2}=-\dfrac{32}{9y^5}.$
Work Step by Step
$\dfrac{d}{dx}(y^3)=\dfrac{d}{dx}(4x)\rightarrow$
$\dfrac{dy}{dx}=\dfrac{4}{3y^2}$
Second Derivative:
$\dfrac{d}{dx}(\dfrac{dy}{dx})=\dfrac{d}{dx}(\frac{4}{3}y^{-2})\rightarrow$
$\dfrac{d^2y}{dx^2}=\dfrac{dy}{dx}(-\dfrac{8}{3y^3})=-\dfrac{32}{9y^5}.$
