Is there any mnemonic to remember 支 and 技?
支 is a hand 又 holding a bamboo branch (half of 竹, or 个). Initial meaning is branch, which became 枝; later on 支 meaning was changed to support/assist possibly because those small branches and sticks were used to help prop up against bigger objects to prevent them from collapsing or falling over.
支 is the phonetic component of 技. Unlikely there is any actual link to meaning of 技, but if you want a sort of mnemonic, you can think of it as this:
A hand holding a bamboo branch and can be manipulated skillfully, and the hand can craft many things with bamboo --&gt; skill, craft.