"His strong sons eat a lot."
Translation:Seine starken Söhne essen viel.
Sein(e) is a "der" word; it takes the same same case and gender forms as the definite articles der, die, das. (Seiner, keiner, einer, aller, are examples of der words) So here it takes the -e ending to indicate the plural.
When a "der" word is different from the nominate singular form, any adjective following it takes an -en to help you see it's changed.
When the der word is unchanged from its nominative singular form, the adjective would take an -e ending. So "der starke Sohn;" "die starken Söhne."
When there's no definite article or "der word", the adjective takes over, and then it has the same endings as a der word would.
Anyway, when you see "die starken" you should think "plural!" And when you see "der starken" it's "feminine dative": "ich rede mit der starken Frau."
-Big 3 get an -e (der, die, das) der alte Mann, das kleine Kind, die schöne Frau
-Changin' gets -en (plural and case changes) den alten Mann (accusative), der schönen Frau (dative), die kleinen Kinder (plural)
-No 'the'? Adjective takes over (no 'der' word or just an 'ein') Kaltes Wetter gefällt mir nicht (das Wetter). Ein guter Mann ist schwer zu finden (der Mann).
Note changin' means the definite article differs -- has changed -- from its nominative singular form (der, die, das). So feminine accusative, for example, doesn't get an -en: "Ich sehe die schöne Katze" -- I see the beautiful cat.
That's true if there's no determiner before "starke" ("Starke Söhne essen viel"), but once you add the "die," things change. The "die" effectively carries that nominative plural "-e" ending, so "starke" doesn't need to, and it uses a sort of "default" ending "-en."
Here's a couple of more comprehensive declension tables that account for the article in front.
I'm not too familiar with the"strong/weak" terminology, but if I remember correctly, "ein" and the possessives use a so-called "mixed" inflection, using some strong endings and some weak endings.
Here's the link in full; if you're using the app, I believe the app just doesn't handle custom-text links very well. (The website, on the other hand, does.) http://germanforenglishspeakers.com/adjectives/adjective-declensions/
"Viel" is not a noun, so it doesn't make sense to put "ein" before it. In fact, "viel" already means "a lot" or "much," so you should just have "Seine starken Söhne essen viel."
(Also you should have an umlaut on "Söhne," or else substitute with "Soehne," though Duo wouldn't mark you down for that.)