Step 1: Recall the sign. The steeple sign is a tapered, pencil-point narrowing of the subglottic trachea on a frontal neck radiograph, resembling a church steeple.
Step 2: Match the disease. This subglottic oedema is the hallmark of acute laryngotracheobronchitis (croup), most often viral and most common in children under 2 years.
Step 3: Recall the clinical picture. Croup has a slower onset than epiglottitis, with biphasic stridor, hoarseness, and a barking (seal-like) cough.
Why the others are wrong: Acute epiglottitis gives the 'thumbprint sign' (a swollen epiglottis) on a lateral film, not a steeple. Laryngeal papillomatosis shows soft-tissue masses, and bilateral abductor paralysis is a clinical and laryngoscopic diagnosis with no steeple.
Ref: Bailey and Love, Short Practice of Surgery, 27th edition, Page 743.