The directional complements 出去 (chūqù) and 出来 (chūlái) both involve movement related to the verb “出” (chū), which means “to go out” or “to come out.” However, their usage depends on the direction of the movement in relation to the speaker or a reference point, and they convey different nuances of movement.
There are many other words like this, such as 进去 and 进来，上去 and 上来, 下去 and 下来, and so on. They can be the directional complements themselves, or verb complements phrases.
Verb + 去 (qù)
It is used to describe movement away from the speaker or from the inside of a place to the outside. It emphasizes the action of leaving the point of reference and moving outward.
e.g.
我要出去走走。 (Wǒ yào chūqù zǒuzou.) I want to go out for a walk.
请把垃圾带出去。 (Qǐng bǎ lājī dài chūqù.) Please take out the trash.
你可以上去看看。(Nǐ kěyǐ shàngqù kànkan.) You can go up and have a look.
他慢慢地走上去了。(Tā mànmàn de zǒu shàngqù le.) He slowly went up.
请小心地走下去。(Qǐng xiǎoxīn de zǒu xiàqù.) Please go down carefully.
太阳慢慢地落下去了。(Tàiyáng mànmàn de luò xiàqù le.) The sun slowly went down.
Verb + 来 (lái)
It is used to describe movement towards the speaker or from the inside to the outside, implying a movement towards the point of reference, often visible to the speaker.
e.g.
月亮出来了。 (Yuèliàng chūlái le.) The moon has come out.
她从房间里出来。 (Tā cóng fángjiān lǐ chūlái.) She came out of the room.
请把这些盒子拿上来。(Qǐng bǎ zhèxiē hézi ná shànglái.) Please bring these boxes up here.
他一听到声音就跑上来了。(Tā yī tīngdào shēngyīn jiù pǎo shànglái le.) He ran up here as soon as he heard the sound.
猫从树上下来了。(Māo cóng shù shàng xiàlái le.) The cat came down from the tree.
你能帮我把那本书拿下来吗？(Nǐ néng bāng wǒ bǎ nà běn shū ná xiàlái ma?) Can you help me take that book down?