to clear, clarify
搞 centers on making something clear by removing confusion or obstruction: to clarify or clear up a matter.
搞 combines 扌 (hand) with 高, which likely contributes the sound and suggests raising or making something prominent, hence clarifying or clearing.
A hand 扌 raising something high 高 to make it clearly visible: the action of clearing or clarifying.
For コウ, imagine a hand clearing a high shelf so you can see everything clearly: high -> コウ.