We say ”木村さんは私にDVDをくれます” ,and also say ”木村さんは私の友達にDVDをくれます” meaning 木村さんgive DVD to my friend (group of us) So when a person give to you or someone that you think he/she is your group such as family, friends, you can say くれます。 In this case, you think リリさん is your group , you can say くれます。リリさん is someone who is not familiar, you should say あげます。but you're リリさん right?, so you can answer　”木村さんは私にDVDをくれます”

> Actually I wrote 木村さんは　リリさんに　DVDをあげます in my answer. You are correct. 你写得对 > But the answer is marked wrong and the teacher said くれます should be used. > 木村さんは　リリさんに　DVDをくれます。 The teache is wrong. "木村さんは　リリさんに　DVDをくれます。" is incorrect. 你的老师写得错 > because I thought くれます is only used when the subject is 私。 But this is not the reason. You use "くれる“ basically when the giver is (regarded to be) positioned in terms of 敬語 higher than the receiver. In most case, it is the situation that "somebody gives something TO ME" . in other words "给我”的时候 木村さんが私にDVDをくれました。 あなたがくれたこのぬくもり あなたが私に愛をくれた。 オレに金をくれる人は、みんないい人だ。 飯（めし）くれ　（给我吃饭 金くれ（给我钱 何かおくれよ(give something to me. Or you can say ： おばさんが子供にプレゼントをくれました。 Here, this child is necesarily your child. くれました is used when the giver is higher than the receiver? Then you can say 社長が部下にプレゼントをくれました ? No, you can't. I don't know why but you can't. So you can practically remember this rule "くれました”只在”给我” (或者”给我自己人”) 的时候, 可以用 **** And this rule makes a very convinient sentece. 「昨日、木村さんがDVDくれたんだ」 This means "Kimura-san gave 'me' a DVD yesterday". you don't have to say "僕に“ nor "私に“. You can tell it from the verb くれる, which shows it is "给我".