"After this you need to be more careful so this doesn't happen again." "Yes, teacher. I'll be more careful from now on."
Viet hasn't been heard of since October 29—Tofugu Day.
After that, the writer stopped drinking alcohol, not even a single drop.
From after, just means after this or from now on.
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.