Stagger means 'moving unsteadily, as if about to fall'.
Options A and C: One cannot stagger below the hill or under the hill.
'Below' and 'under' both refer to the layer or level below the hill. The meaning formed 'stagger below' and 'stagger under the hill' seems vague. Hence options A and C are incorrect.
Option D: 'Off' means 'no longer attached or connected to something'. When used here, it means that the person is staggering (moving unsteadily) and unconnected to the hill. This sounds unnatural, one cannot stagger off the hill. Hence D is incorrect.
Option B: 'Down' means 'from a higher to a lower point'. It is relevant to the given sentence.
Since it is a hill, it can
only make sense to stagger down the hill because the hill is an elevated
structure and might be difficult to travel through. Hence, the correct
option is B.