Translation:There are a lot of rocks in these parts.
It still needs clarification given that "in these parts" and "from these parts" are both allowed as correct answers and do not convey the same meaning. I would think "in queste" and "da queste" would be the respective translations and so the 'around here' is wrong and should really be 'from around here'.
I also thought it should mean from but it seems to be idiomatic: http://www.wordreference.com/iten/da%20queste%20parti
"da queste parti" = "in this vicinity"
Google Translate says in these parts and around here.
No! There is a lot of sand/rice/rock/stone but there are a lot of grains/rocks/apples etc. In the first case the noun is uncountable and singular even when you are talking about a large quantity. In the second case the noun is countable and when there is more than one you use the plural. Note the word rock (and stone) can function as either depending on whether you are talking about individual countable pieces or not.
On the question you asked: the rule is that the verb agrees with the number of the thing there is lots of, whether you say "a lot of" or "lots of" (the two are interchangeable). There are a lot of languages; there are lots of languages; there is a lot of work to do; there is lots of work to do. A lot of words were written; lots of thinking was needed etc
Your translation sort of conveys the sense of the sentence but you are changing the whole grammatical structure of it. You are substituting the sentence "it is rocky" and they asked you to translate "there are rocks".
Ci sono molte rocce. There are lots of / many rocks.
È molto roccioso. It is very rocky.
Duolingo wants you to stick to the basic structure: "There are . . . " vs "It is. . . . " Best wishes.