No, you actually use the «у» preposition + genitive.
«У» has a number of uses. You must have seen it in the sentences like «у меня́ нет кни́ги» 'I don't have a book' (you could understand it as 'at my place, there's no book' if that helps).
Listen more closely: Анна stresses the first consonant and она stresses the second. Duo has been consistent with these different pronunciations since the 'Alphabet' basics.
Boredom does tend to result from stunted observations. Or maybe you just need headphones... like Duo keeps suggesting.