They managed to ______ the contract despite several obstacles.

Option 1: pin down → Means to find exact details or force someone to make a decision. "Can you pin down the exact date?" Doesn't fit — the sentence is about successfully completing something, not finding details.

Option 2: write off → Means to dismiss something as a failure or loss. "Don't write off your chances of winning." This is the opposite — they actually succeeded!

Option 3: pull off → Means to succeed in doing something difficult. "She pulled off a surprise party even though keeping the secret was hard." The sentence says they "managed to" do something "despite several obstacles," which clearly points to succeeding at something challenging. ✅

Option 4: think through → Means to carefully consider all parts of something before acting. "Think through your answer before writing it down." Doesn't fit — the sentence is about achieving something, not just thinking about it.

Hence, pull off is correct. The clues "managed to" and "despite several obstacles" tell us they succeeded at something hard — and that's exactly what "pull off" means. "They pulled off the contract" = they got it done despite all the problems.