How do I answer this question

I understand the mechanism but how am I supposed to work out the structure of methyl cinnamate?

I understand the mechanism but how am I supposed to work out the structure of methyl cinnamate?

If that is all you have to go on, then you don't need to show the whole structure.
Just show the relevant functional group to detail the mechanism and use a bunch of R's to show the rest of the molecule.

Well - in that part of the question at least, you aren’t expected to work out the structure - Pigster has already very correctly pointed out that you can draw a C=C double bond with a bunch of R’s attached.
If you were expected to work out the structure, you would have been given stuff like NMR spectra (or rather a table with NMR data), although you probably could try to work out a very imprecise structure from the name and this wouldn’t be much help (i.e methyl cinnamate implies a methyl ester, so -COOCH3 must form part of the structure and since the formula is given as C10H10O2, you can deduce the rest of the molecule must have the formula C8H7, so C8H7COOCH3 is maybe about as far as you can get - that said, since the question hints at there being an alkene, you might be able to deduce that strictly it is C6H5CH=CHCOOCH3, but you’d need to know whether the alkene is E/Z and find a convincing reason why it isn’t C6H5C(COOCH3)=CH2 or something else).

Well - in that part of the question at least, you aren’t expected to work out the structure - Pigster has already very correctly pointed out that you can draw a C=C double bond with a bunch of R’s attached.
If you were expected to work out the structure, you would have been given stuff like NMR spectra (or rather a table with NMR data), although you probably could try to work out a very imprecise structure from the name and this wouldn’t be much help (i.e methyl cinnamate implies a methyl ester, so -COOCH3 must form part of the structure and since the formula is given as C10H10O2, you can deduce the rest of the molecule must have the formula C8H7, so C8H7COOCH3 is maybe about as far as you can get - that said, since the question hints at there being an alkene, you might be able to deduce that strictly it is C6H5CH=CHCOOCH3, but you’d need to know whether the alkene is E/Z and find a convincing reason why it isn’t C6H5C(COOCH3)=CH2 or something else).

There is no way you can work out the structure with the information provided. You can only tell it is a methyl ester. If it reacts with bromine in the dark, then it is most likely that the compound contains a double bond which undergoes electrophilic addition reaction with bromine. Then write down the mechansim in the usual way.

Oh I absolutely agree - I just don’t think I articulated my explanation as to what the problem is with trying to work out the structure is very well.
To clarify what I meant, the question tells you the molecular formula, that there is a methyl ester and implies an alkene should be present. From that, it is possible to work out that there is a benzene ring (i.e by subtracting things off the given formula and seeing what you are left to work with) - you just have no way of knowing what is bonded to what and even if you do spot the right structure, there are plenty of other possible ways the things could be bonded.