What makes this question tricky is the vocabulary. If you don’t know the meaning of the words, you have no choice but to make an educated guess.

First blank:

A derivative makes no sense in the context of the first blank. An uncontroversial contradicts the context of the first blank because it requires a word that is opposite to the word traditional. Although I don’t know what iconoclastic means, I have to pick it because the other two don’t fit.

Second blank:

I have no idea what hackneyed means. I also don’t know what euphonious means but it reminds me of the word euphemism, so I tend to think it is a positive word. Heterodox fits well because this blank requires a word that would describe something that would upset people who are traditionalists.

Correct answer: an iconoclastic/heterodox