You have to use the quotient rule which states:

\(\frac{d}{dx}[\frac{f(x)}{g(x)}]=(g(x)f'(x)-g'(x)f(x))/(g(x))^{2}\)

So

\(\frac{d}{dx}[\frac{8}{3x^{4}}]=\frac{3x^{4}\times0-12x^{3}\times8}{(3x^{4})^{2}}\)

Simplifying that, we get:

\(\frac{-32}{3x^{5}}\)

\(\frac{d}{dx}[\frac{f(x)}{g(x)}]=(g(x)f'(x)-g'(x)f(x))/(g(x))^{2}\)

So

\(\frac{d}{dx}[\frac{8}{3x^{4}}]=\frac{3x^{4}\times0-12x^{3}\times8}{(3x^{4})^{2}}\)

Simplifying that, we get:

\(\frac{-32}{3x^{5}}\)