Answer:
a) 勅 -> 加 -> 吐 -> 堀
勅 CHOKU - imperial decree
加 KA, kuwa(eru), kuwa(waru) - add, append, join, take part
吐 TOU, ha(ku) - spew, vomit, give vent to
堀 hori - moat, canal, ditch
b) 案 -> 棋 -> 期 -> 脚
案 AN - plan, proposal
棋 KI - go, shogi, Japanese chess
期 KI, GO - time, period, term
脚 KYAKU, KYA, ashi - leg