She was quite upset with the idea _____________________ the project.

The correct answer is "of changing." In English, certain verbs and adjectives are commonly followed by specific prepositions. In this case, the pattern "upset with the idea of" is the appropriate construction to express that someone feels negative emotions regarding the concept of something happening—in this case, changing the project.

The phrase "the idea of" is used to introduce a concept or thought, and when paired with a gerund (the -ing form of a verb), it indicates that the emotional response is directed toward that action or change. Thus, "of changing the project" effectively communicates that her feelings of upset are specifically about the alteration of the project conceptually.

Other constructions may not fit grammatically or semantically in this context. For example, "for changing" suggests a reason for being upset, while "to change" implies an intention and does not capture the concept of being emotionally affected by a proposed idea. Similarly, "with changing" does not align with standard usage patterns in English related to feelings about ideas or concepts.