"Nowadays, children no longer eat vegetables."
Translation:כיום, ילדים כבר לא אוכלים ירקות.
It's an inflected form of אין ("there is not"), pronounced "einam", and it's a flowery way of negating a sentence like this. You usually hear it in songs or poems, not so much in everyday life.
So instead of "אנחנו לא צריכים לעבוד" you can also say "איננו צריכים לעבוד", for example. See the full inflection table here: https://en.wiktionary.org/wiki/%D7%90%D7%99%D7%9F#Inflection
כיום, ילדים לא אוכלים יותר ירקות. On its face, this sounds like "Nowadays, children don't eat more vegetables." It's not what they're asking for. Am I right? From this discussion, I see that יותר could mean "no longer", but that doesn't seem to fit into this sentence clearly. Perhaps לא יותר would do it better to my ear.
I got this English sentence in a "Mark all correct translations" exercise and the translation above was not one of the choices. Instead they offered both כיום, ילדים אינם אוכלים ירקות יותר and כיום, ילדים לא אוכלים יותר ירקות as acceptable translations. Neither of these seems as good.