government office
廨 refers to a government office, the physical place where official administrative work is carried out.
廨 combines 广 (building with a roof) and 解, which likely contributes the sound. The character originally denoted a type of government office or official building.
Under the roof of a building (广), officials untangle and solve (解) administrative matters — that is a government office.
For カイ, imagine a government office by the sea (海, かい): the sound of the waves reminds you of カイ while you work inside the building.