To Fill Out
To Write In
transitive verb, godan verb
You write something on this paper but it is crowded. Why is it crowded? Because there are little boxes for you to write things in. You are filling out a form, which makes this verb to fill out or to write in.
かきこむ
The reading comes from 書く and 込む combined into one.
急いで申込書に書き込んだ方がいいよ。あと十分で事務所は閉まっちゃうんだから。
You better hurry up and fill out an application. The office will close in ten minutes.