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: 
We know the [chain rule](http://en.wikipedia.org/wiki/Chain_rule) for differentiating functions of functions 

$$\frac{\text{d}y}{\text{d}x} = \frac{\text{d}y}{\text{d}u}\cdot \frac{\text{d}u}{\text{d}x}$$

So for your example let $u = 4x$, the bit inside the bracket. Now 

$$\begin{align}
\frac{\text{d}}{\text{d}x} 8 \cdot \sin(4x) &= 8 \cdot \left(\frac{\text{d}}{\text{d}x} 4x \right) \cdot \left(\frac{\text{d}}{\text{d}u} \sin(u)\right) \\
& = 8 \cdot 4 \cdot \cos(u)\\
& = 32 \cdot \cos(4x) 
\end{align}$$

I've shown all the steps but with with a little bit of practice most most people can jump straight to the last line.
$$y' = 8\*4(\cos 4x)$$
$$y' = 32\cos 4x$$