The question is really asking which non-depolarising blocker you can give safely when both the liver and the kidney are not working well. The clues are a high bilirubin (8 mg/dl) and a high creatinine (1.9 mg/dl).
Think about how each drug leaves the body. Pancuronium and vecuronium both lean on renal excretion, and vecuronium also uses biliary excretion, so a damaged kidney or liver makes their effect last far too long. Rocuronium is mostly handled by the liver, so a jaundiced patient will stay paralysed longer than expected.
Atracurium breaks down on its own through Hofmann elimination, a spontaneous chemical degradation at normal body pH and temperature, plus ester hydrolysis in plasma. Neither pathway needs a functioning liver or kidney. That makes its duration predictable even when both organs fail, which is exactly this patient's situation.
So the safe pick is atracurium.
\[\boxed{\text{Atracurium}}\]