"zeh" reminds me a lot of the Polish "to". It acts like a copula or an equal-sign.
It's been four months, so I'll propose an answer.
Without זה, the sentence (to me) would sound like "Plate not food." With the זה, to me the sentence becomes "A plate: this is not food."
Now that I've typed that out, I think that doesn't make sense. So it's just a grammar thing.
I think it's more accurate to say that with the word זה the sentence becomes - A plate is not food. The word זה 'plays the role' of the English 'is', although they have a different meaning. That's due to the differences of sentence construction between the two languages.
Is 'zeh' not close to "this"? Would the sentence צלחת הוא לא אוכל mean the same thing? Or can you say that at all?
Whats wrong with the sentence? A have wrote exactly as "correct" answer you offer me in red. Only difference is stop sign at the end of sentence.
Due to this I cannot end my lesson. we are just going on a circle offering me mistake with completely same sentence I wrote...