catch, arrest
拿 centers on physically seizing or taking hold of something: catching or arresting a person or thing.
拿 combines 合 (fit, join) on top and 手 (hand) on the bottom, suggesting a hand closing around something to catch or arrest it. The exact historical development is uncertain, but the component arrangement likely reflects the idea of a hand grasping.
The top 合 looks like a lid fitting onto a container, and the bottom 手 is a hand. Imagine a hand clamping down like a lid to catch or arrest something.
For ダ, picture a hand catching a dart mid-air: dart -> ダ, and the hand seizes it firmly.