This medicine will stimulate your digestion.
Koichi's having a touch of diarrhea, so please have him eat something easy to digest.
I haven’t finished digesting the ramen I ate for lunch.
What is something that will first extinguish something and then change it? One thing I can think of is your body. It takes in food, extinguishes it in your stomach, then changes it into things your body can use (and then excrete). That's why this "extinguish-change" process is your digestion.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.