交代
こうたい · koutai · JLPT N2 · noun
relief
交 = exchange + 代 = substitute: one swaps in to take over from the next
The same 交 appears in 交換 (exchange) and 代 in 代理 (proxy). Together they describe one party handing a duty over to another, like passing a baton in a relay.
交 — top 亠 + 父-like crossed legs
Originally a pictograph of a person standing with legs crossed, showing the idea of crossing or intersecting. From this concrete image, the meaning extended to abstract senses like 'exchange,' 'interact,' and 'hand over.' Modern uses such as 交流 (exchange) and 交通 (traffic) all trace back to this core notion of crossing.
代 — person radical 亻 + 弋 (stake/dart, phonetic)
代 is a semantic-phonetic compound: 亻 (person) gives the meaning and 弋 supplies the sound. The original sense was one person taking the place of another, which broadened to 'substitute,' 'replace,' and then 'generation' or 'era' — successive groups of people replacing the previous.