OE

A, B

The fact that the blank is the word that begins the sentence may make this question more challenging than a typical Sentence Equivalence question. The first clause is fairly direct; he passed on the project, and the blank will contain an adverb to describe this decision. The second clause contains the detour road sign “notwithstanding,” which means “despite.” “Professed,” which describes his support, means “stated,” so you know he passed on the project despite his vocal support. Therefore, you can predict the first blank to be something like surprisingly or paradoxically. Choices (A) counterintuitively, “contrary to intuition,” and (B) unexpectedly both match that prediction quite well. They both create sentences pointing out the subject’s seeming inconsistency.
Three of the other choices could work on their own in this context: (C) self-indulgently, “to indulge one’s own desires,” (D) obscurely, “vaguely,” and (E) pusillanimously, “cowardly,” all characterize the way in which one could decline a project, but none logically contrast with “professed support.” Choice (F) punctiliously, “attentive to detail,” does not make sense in this context. Only (A) and (B) logically complete similar sentences.