What is the grammar behind 没四百下不来 Ok so I recently heard the phrase on a tv show 


  没四百下不来


I kind of intuitively understand in the context that it meant that not even 400元 could buy the flowers that they were discussing. 

However, exactly how this grammar works I'm not sure.What is the construction here and how is it used?
Actually your interpretation is not exactly correct(Although pretty close). The sentence means 400 yuan will be approximately sufficient(still probably a little bit too high or too low) to buy the stuff.

This is quite an oral expression(more commonly seen in northern China). But you can interpret it this way: “拿下来” means "get/fetch/catch something", a connotation which can also be expanded to "buy something"(e.g. get the ownership of something). In this sentence, “下来” can be seen as a shorthand for “拿下来”. And therefore “下不来” is "unable to get", the "不" in the sentence signifying negation(cannot, unable to). And the whole sentence therefore is "Without (at least) 400 yuan you cannot buy it". This should now make sense to you.