"Ella necesita lavarse las manos antes de la cena."
Translation:She needs to wash her hands before dinner.
In Spanish, names of parts of the body are frequently preceded by the definite article (el, la, los or las, meaning "the") instead of possessive adjectives (such as mi for "my" and tu for "your"). In most cases, the possessive adjective is used only where the context doesn't make clear whose body is being referred to.
We normally don't use "sus manos" when we are speaking. So it isn't a literal translation and Duolingo should accept both answers.