exchange
兌 centers on the idea of exchange: giving one thing and receiving another in return.
The historical origin of 兌 is uncertain. It visually contains 八 and 兄, but these components may not directly reflect the original formation.
The top 八 suggests division or separation, and the bottom 兄 (older brother) can be seen as a person. Imagine an older brother dividing goods to make an exchange.
For ダ, picture exchanging a dull item for a shiny one: dull -> ダ, and the exchange makes it better.