flat cap; hunting cap
A soft, round cap with a small stiff brim in front, often made of tweed or similar fabric. Commonly worn in casual or vintage styles.
祖父はよくハンチング帽をかぶって散歩に出かける。
My grandfather often goes for a walk wearing a flat cap.
ハンチング帽 is the full, unabbreviated form for the flat cap; ハンチング alone is the common everyday abbreviation for the same item.
From English 'hunting cap', with ハンチング as a wasei-eigo shortening of 'hunting', combined with 帽 (ぼう, 'cap').