The audio for this sentence isn't great. The "в" is supposed to be pronounced.
Из takes genitive case. В and На take Prepositional (where something is located) or Accusative (where something is going).
I don't understand why the more concise "Moscow has many schools." isn't accepted.
Technically the sentence does have "in" in it (в), so a slightly different meaning.
In correct translation the options should be either: There are many schools in Moscow" or There is a lot of schools in Moscow", since the word "lot" is singular. It can also be translated as "There are lots of schools in Moscow". DUO's choice is grammatically incorrect in this case.