He was sixteen years old and didn't have a care in the world.

care 在这里指"忧虑、烦恼"，通常指需要操心或担忧的事情。 don't have a care in the world 是固定表达，字面意思是"在这个世界上没有任何需要操心的事"，引申为"无忧无虑"的状态。