"The boy's hats are big."
Translation:Die Hüte vom Jungen sind groß.
The noun for boy is known as a weak masculine word. In this case, they are declined differently. Look at this link and look under "weak declension". Sometimes you can spot weak masculine words by finding a masculine word that ends with an "e". Affe, the word for ape, is another example. I hope this helps!
Hute should have an umlaut "Hüte". Jungend should be "Junge". Duo doesn't recognize "ss" for "ß". There is only one boy, with many hats. So there is no "die" to turn into "der" in genitive.
"Die Hüte des Jungen sind groß."
I'm not a native speaker, but I believe "Jugend" means "youth" or "young people". Not specific enough for "boy".
Generally, the genitive construction is preferred. In this specific example, it doesn't make much of a difference, though – as long as you don't contract the 'von dem'. To my ears both "Die Hüte von dem Jungen" and "die Hüte des Jungen" sound fine. If you also use the inverted word order ("Des Jungen Hüte"), it sounds rather stilted. Note that it's "des Jungen" in genitive. The one thing I wouldn't use here is duo's 'Die Hüte vom Jungen'. The combination 'vom'+dative really sounds awful.