With countable nouns (可算名詞), we use many, regardless of whether the sentence is grammatically positive or negative, or a question:
- (+) She's got many friends.
- (-) She has not taken TOEFL many times.
- (Q) Will you apply to many schools this year?
You can substitute a lot of in any of the above sentences.
But with uncountable nouns (不可算名詞), we use a lot of in grammatically positive sentences:
- (+) I have a lot of time this week.
- (+) He made a lot of money last year.
However, we can use much or a lot of in grammatically negative sentences and questions:
- (-) I don't have much time this week.
- (-) I don't have a lot of time this week.
- (Q) Did he make much money last year?
- (Q) Did he make a lot of money last year?
Please use English well!