What does this sentence mean?
They would likely be interested in what you've put together here!
When I should use this?
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"What you've put together here":
The phrasal verb "put together" is used more often than its synonyms when the object is something written—e.g., research, a report, or a proposal. So a speaker describing such items would be more likely to use this phrase than another. "Put together" also implies that the assembly required effort or creativity.
You make a list of interesting questions on ell.stackexchange.com and show it to me. I know a friend who could use it. The list is a thing, we are already talking about it, and you assembled it. Further, the list is the written outcome of research, and it took effort. Therefore, I could say, "They would likely be interested in what you've put together here!"
You and I work at a company. You write a contract that will reduce what a customer pays but keep our profit the same, and you e-mail it to me. The contract is a thing, it is the topic of conversation when I reply, and you constructed it. Additionally, the contract is a written proposal, and it took creativity. Therefore, I could say, "They would likely be interested in what you've put together here!"
You and I are filling candy bowls. You mix chocolates and hard candies together in a bowl, and I know a friend who likes that combination. The mix is a thing, it is nearby, and you created it. But it is not something written, nor did you need much effort or creativity to make it. I could say, "They would likely be interested in what you've put together here!", and I would be understood. But the word choice would be poor, unless I say it jokingly, acting like you are clever for inventing the combination.