To Drop Something
To Let Something Fall, To Lose Something
transitive verb, godan verb
You've seen how 落ちる means "to fall down." Now you're doing the action of "falling something down," aka you're dropping it. You can remember this because you kind of toss (とす) something and it drops to the ground, making this word mean to drop something.
The reading comes from 落ちる. So long as you know that word you can apply that reading over here, too.
あの、ハンカチ落としましたよ。
Oh, you dropped your handkerchief.
そんな信用を落とすようなことは今すぐ止めた方がいいよ。
You should immediately stop doing things that will make people lose faith in you.
今日、『男を落とす方法』っていう本を買ったんだけど、帰り道にどこかで落としちゃったみたいなんだよね。
Today I bought a book called 'How to Make a Man Fall In Love With You,' but I lost it somewhere on the way back home.