Answer:
a) 動 -> 加 -> 吐 -> 増
動 DOU , ugo(ku) - move
加 KA, kuwa(eru), kuwa(waru) - add, append, join, take part
吐 TOU, ha(ku) - spew, vomit, give vent to
増 ZOU, ma(su), fu(eru), fu(yasu) - increase, rise, raise
b) 弦 -> 畜 -> 累 -> 紀
弦 GEN, tsuru - string, bowstring
畜 CHIKU - animal raising, domestic animal
累 RUI - involvement, trouble, accumulation
紀 KI - narrative, history