I think that diagramming this argument will help us to understand it.
Premise: Anyone who believes in democracy (BD) has a high regard for the wisdom of the masses (HR).
BD - - - - - - - - -> HR
The contrapositive tells us: If someone does not have a high regard for the wisdom of the masses (not HR), then that person does not believe in democracy (not BD).
not HR - - - - - - - - - - - > not BD
Premise: Griley is an elitist who believes that popular artwork is unlikely to be good (UTBG).
Conclusion: Griley does not believe in democracy.
What does Griley's opinion on popular art have to do with democracy? This seems to be a hole in the argument. We need to find an answer choice that completes the argument. I'll diagram answer choice B to demonstrate why it is the correct answer.
B. Anyone who believes that if an artwork is popular it is unlikely to be good (UTBG) does not have a high regard for the wisdom of the masses (not HR).
UTBG - - - - - - - - > not HR
Now, using our contrapositive from above, we can finally link the arguments.