Final answer:
The word 'mollify' best fits the sentence, suggesting that her demeanor had a calming effect on her opponents.
Step-by-step explanation:
Her friendly manner and disarming smile helped to mollify those who opposed her views on the proposal. The correct choice is (d) mollify, which means to soothe in temperament or reduce in intensity. This choice best matches the context of the sentence as it indicates that her friendliness and smile had a calming effect on those with opposing views.
The other options presented are: appease, which also means to calm but often by conceding something; antagonize, which means to provoke or cause to become hostile; and confound, which means to confuse. Neither of these words fit the intended meaning of the sentence as well as 'mollify' does.