It may not seem like much of a difference, but adjective placement is important. Adjectives generally live next to the noun they modify if that helps.
Muchos adultos aquí son jóvenes.= Many adults here are young. (Of the adults in this location, many are young. Stressing age.)
Muchos adultos jóvenes están aquí = Many young adults are here. (There are a lot of young adults at this place. Stressing location.)
The old cat is white. = El gato viejo es blanco.
The white cat is old. = El gato blanco es viejo.
This is especially important with words like "only" which can change the meaning of the sentence depending on where they're placed.
I want a new bike. (A simple statement of fact.).
Only 'I' want a new bike (no one else wants one).
I only 'want' a new bike (I don't want anything else).
I 'want' only a new bike (not a ball or a puppy... Though this is not traditional English phrasing).
I want only 'a new' bike (not an old bike).
I want a new 'bike' only (not a new bat or new ball).
I see this sentence as: In this place(here), there are many adults; further distinguishing. A lot of the adults in this place(here) are young. Therefore, many young adults are inhabiting, occupying this space place(here). So, Many young adults are here, should also be accepted as a reasonable response.
It's a logical conclusion, but it's not what the Spanish sentence wants to focus on. The original sentence focuses on the age of the adults here: many of them are young. Your sentence shifts the focus instead on the whereabouts of young adults: many of them are here. Those two sentences answer different questions.
The Spanish sentence is telling us a quality of the adults while your sentence talks about the existence of young adults. Both sentences lead to the same result, young adults here, but focus on different aspects.
Your sentence would translate as "Hay muchos adultos jóvenes aquí."
There's not a great difference in meaning between aquí and "de aquí". It's basically the same difference as in English:
- los adultos aquí - the adults here
- los adultos de aquí - the adults from here
Basically, aquí talks about the things that are here at the moment, and "de aquí" talks about the things that come from here.