。
The boy fanned himself with his hat.
Literal
Boy [topic-は] hat [with-で] himself [object-を] fanned
で marks the hat as the instrument of the action. 煽ぐ (あおぐ) means to fan (to move air over) — distinct from 煽る (to fan flames / incite). 自分 as the object of the verb is an explicit reflexive, even though context alone would have implied it.