$ (\sqrt[3]{4})^{-2} \times (\sqrt[3]{-2})^{-2} =(\sqrt[3]{4} \times \sqrt[3]{-2})^{-2} = (\sqrt[3]{-8})^{-2} = (-2)^{-2} = \frac{1}{(-2)^2} = \frac{1}{4}=4^{-1} $