Alessia è una ragazza davvero piena d’idee: ________ viene una al giorno.

 

The sentence is:
Alessia è una ragazza davvero piena d’idee: ________ viene una al giorno.

The correct answer is c) gliene.

Explanation

• gliene is a combined pronoun: gli (to her/him) + ne (of them, referring to "idee"), so gliene means "to her, of them".

• The complete meaning is: "One (idea) comes to her per day" or "She gets one of them (an idea) per day."
  In Italian, the use of gliene is the standard way to combine indirect (person) and partitive (of ideas) pronouns.

• le ne is ungrammatical; two direct pronouns cannot be combined like this.

• gli alone is missing the partitive "ne" and would just mean "to her/him".

Structure

• gliene viene una (di idea) al giorno = to her, of them, comes one per day.

• This construction is common in Italian when speaking about ideas, news, or similar abstract things arriving or occurring to someone.

Summary:
Gliene is grammatically correct and idiomatic in this sentence as a double pronoun, which is typical when talking about ideas (or objects) coming to someone.