"They show their shoes."
Translation:De visar sina skor.
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It should. But it has a different meaning. Swedish has reflexive possessive pronouns - "They show their shoes" can be translated to
"De visar sina skor." -- sina refers to the subject, de: they are showing their own shoes.
"De visar deras skor." -- deras refers to some other people, not the subject de: they are showing some other people's shoes.
In English the sentence is ambiguous, in Swedish we don't have that ambiguity.
If the pronoun refers to the subject in the same clause, it's sin/sitt/sina. If it refers to someone/something other than the subject, it's hans/hennes/deras.
In more complicated sentences this rule is often no help and you can arguably use either and people have written at length about it. Plenty of native speakers confuse the two even in simple sentences, so don't worry too much about it.
It wasn't until I started using Duolingo that I realised how frustrating it can be that we don't have separate pronouns for "their own" and "their" (another person's). I came across this problem the other day and had to reword the whole sentence so that I could show I was talking about two different people's possessions!
I don't understand... we were asked to translate "they show their shoes," which doesn't specify whether "they" are showing "their own" shoes or someone else's shoes. Given the ambiguity of the English sentence, shouldn't both "sina" and "deras" be accepted as plausible translations?
 see my reply below