"His strong sons eat a lot."
Translation:Seine starken Söhne essen viel.
In Nominative in case of no article the ending of the adjective before the plural noun should be -e. Why in this case, the ending is -en
You need starken here. If you wrote 'starke', that would have been incorrect, and Duolingo would have then shown you a correct alternative (which includes kräftigen as a possibility). It doesn't always successfully choose the 'nearest' correct answer, unfortunately...
Why it should be starken (not starke), please explain it. (the ending of adjectives in Nominativ case before plural nouns is -e)
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.