Step 1: Read the clinical picture. Bilirubin 8 mg/dl points to significant hepatic dysfunction, and creatinine 1.9 mg/dl points to impaired renal function. The ideal relaxant is one that does not depend on the liver or kidney for clearance.
Step 2: Recall the elimination routes. Atracurium is cleared by Hofmann elimination and non-specific plasma ester hydrolysis. Both are organ independent, so its clearance is unchanged in hepatic and renal failure.
Step 3: Eliminate the wrong options. Vecuronium is partly excreted in bile and partly renally, so it accumulates in hepatic and renal disease. Pancuronium is largely renally excreted and is strongly prolonged in renal failure. Rocuronium is mainly cleared by the liver, so its action is prolonged with raised bilirubin.
Step 4: Match drug to patient. With both liver and kidney impaired \(\left(\text{bilirubin}=8,\ \text{creatinine}=1.9\right)\), only organ-independent clearance is safe.
The answer is C. Atracurium.