Errand
Business
noun
A task action is something you have to do (because 事 is all about actions). What's another way to say "an action that is a task," though? I would say errand or even business.
ようじ
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.
用事をおねがいしてもいいですか。
Would you mind if I asked you to do some errands?
ごめんなさい！ちょっと用事が出来てしまって、今日のレッスンをキャンセルしないといけなくなってしまいました。
Sorry! I have to take care of something and I have to cancel my lesson today.
大事な用事があるので、明日は出勤することができません。
I have an important matter to attend to so I will not be able to work tomorrow.