The sentence I am talking about is ジュースが出る大きいな桃 .
I don't understand why 大きいな桃 is written at the end. I would say something like:
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ジュースが出る大きいな桃 comes from a news headline and it is not a full sentence. Just like in English headlines you don't normally write full sentences.
It's simply a noun phrase: a description of a peach.
Big peach that juice comes from.
I haven't read the article but (from the picture) you might imagine the full sentence would be something like "There is a shop with a big peach that juice comes out of". Not a very snappy headline.
Maybe I should explain the grammar too. 桃 is being modified by two things. The first is a simple na-adjective, 大きな (note that there is a typo in your sentence 大きいな). The second is a full sentence called a relative clause ジュースが出る. In Japanese full sentences/phrases can modify nouns just like adjectives.