The word "parents" should have an apostrophe on the end, as a plural noun showing possession.
Duolingo has a problem displaying trailing apostrophes in the word bank tasks.
"svůj" can get translated as - můj (my), tvůj (your sg), jeho (his, its), její (her), náš (our), váš (your pl), jejich (their)
You use "svůj" in a situation where personal pronoun and possessive pronoun match (ie. I - my; you sg - your sg; he - his; she - her; it - its; we - our; you pl - your pl; they - their). "I have my car. Já mám svoje auto.; You have my car. Ty máš moje auto.; etc." I can go on, but I guess you get the point.
There is one situation where you need to be careful, because 3rd person sg and plural (he-his, she-her, it-its, they-their) can be ambiguous in English.
He does not see a car of his parents. (In Czech this sentence gets translated as "On nevidí auto svých rodičů." -> meaning a car of his own parents; or "On nevidí auto jeho rodičů." -> meaning a car of parents of another guy).