The sentence describes Claire's moods shifting quickly from one extreme to another.
(i) The first blank describes a lively, energetic mood:
- (C) ebullient means cheerful and full of energy, which fits well.
- (A) prolific means productive, not about mood.
- (B) dysphoric means uneasy or unhappy, which contrasts with lively but is better suited to the second blank.
(ii) The second blank describes a quiet, sad mood:
- (F) despondent means very sad or hopeless, fitting the forlorn look.
- (E) taciturn means habitually quiet, which works but is less about sadness.
- (D) unflappable means calm and not easily upset, which doesn't fit a forlorn mood.

The best fit is (C) ebullient for (i) and (F) despondent for (ii).
Final sentence:
Claire's moods shifted drastically and unexpectedly - one moment she was ebullient, chatting lively, the next she was despondent, looking forlornly out of the window.