What is the best sequence of reactions for the preparation of p-bromostyrene from ethylbenzene?

I'd brominate the ring first with ferric bromide and bromine. You'd get both ortho and para substitiution so you'd have to do a separation, but once you isolated the 4-bromo derivative, bromination with N-bromosuccinimide, followed by base treatment in ethanol should give you the desired compound. The 4th answer won't work, nor will the first. And I don't like radical bromination for this as it is too unselective, so I'd eliminate 3. So you're stuck with 2 (but there are better synthetic routes if you don't have to stick to these 4 choices).