The cube root of -0.064 is:

1. -0.8

2. 0.8

3. 0.4

4. -0.4

$\sqrt[3]{-0.064}\\[1em] = \sqrt[3]{-\dfrac{64}{1000}}\\[1em] = {-\dfrac{\sqrt[3]{64}}{\sqrt[3]{1000}}}\\[1em] = {-\dfrac{\sqrt[3]{4 \times 4 \times 4}}{\sqrt[3]{10 \times 10 \times 10}}}\\[1em] = {-\dfrac{4}{10}}\\[1em] = -0.4$

Hence, option 4 is the correct option.