The hour hand moves at (1/2)° every minute
The minute hand moves 12 times as fast = 6° every minute
From 12 Noon....the hour hand has moved (1/2)° (48) = 24°
The minute hand has moved (6°) (48) = 288°
The larger obtuse angle between them = (288 - 24)° = 264°
The smaller obtuse angle between them = (360 - 264)° = 96°