"Were you eating in the private cafe."
Translation:O'ch chi'n bwyta yn y caffi preifat?
Many building and workplaces are also feminine and are introduced with mewn, meaning in a. The difference between yn and mewn is that yn is a very specific place, whilst mewn means any old place and in a. Yn is also used when saying in the (yn y).
This sentence has "in the", not "in a", and so mewn seems inappropriate to me.
Always a good idea :)
It took me a bit to find again because that statement about the difference between mewn and yn is sort of tucked away in the middle of a paragraph -- if I wasn't sure I had read it before, I might have skipped right over it while trying to find it again.