mooring stake, painter, mooring
牁 centers on securing a boat: a mooring stake or painter used to tie up a vessel. The mooring sense is the core action of fastening to a fixed point.
牁 combines 爿 (a split wood or bed component) with 可, which likely contributes the sound. The character is associated with a stake or post for mooring, but the exact historical development is uncertain.
The left side 爿 looks like a wooden post or stake, and the right side 可 suggests something permissible or possible. Imagine a wooden stake that makes mooring possible: 牁 is the stake you tie your boat to.
For カ, picture a car (カ) being moored to a stake: car -> カ, and the stake holds it in place like a boat.