Step 1: The skull radiograph shows a thickened diploe with ill-defined fluffy sclerotic areas, described as a cotton-wool appearance, most pronounced in the frontal bone. These features are characteristic of Paget disease of bone.
Step 2: Paget disease is a chronic disorder of excessive abnormal bone remodelling affecting the skull, pelvis, spine and long bones. In the skull it produces osteoporosis circumscripta in the early lytic phase, then coarsened trabeculae and the mixed lytic-sclerotic cotton-wool pattern with diploic widening.
Step 3: The distractors differ. Multiple myeloma gives multiple well-defined punched-out lytic lesions. Osteosarcoma shows an aggressive bone-forming destructive lesion, uncommon in the skull. Osteomyelitis shows infective destruction with periosteal reaction. The cotton-wool diploic thickening points to Paget disease (option a).