Integrate: $\int \limits_0^{z/4} \sin ^4 (2x)dx$

Question

$$\begin {array} {1 1} (a)\;\frac{z}{16} \\ (b)\;\frac{3z}{32} \\ (c)\;\frac{5z}{16} \\ (d)\;\frac{3z}{16} \end {array}$$