Question: I have forgotten the steps to do this so step by step working out would be appreciated. Multiple ways of doing would also be good to see which method works best for me.

Answer: 
Let $f(x)=8\sin(4x), g(x)=4x$.
Then, 
$$f^\prime(x)=[8\sin\{g(x)\}]^\prime=8\cos\{g(x)\}\cdot g^\prime(x)=8\cos(4x)\cdot 4=32\cos(4x).$$
$$y' = 8\*4(\cos 4x)$$
$$y' = 32\cos 4x$$