Sure, here are the sentences completed with the correct phrasal verbs:

11. Can you **turn off** the lights when you leave the room?
12. I need to **cut down on** my expenses if I want to save money.
13. She **carries on** the tradition of making handmade crafts to her children.
14. After the trip, they will **go back** to their hometown.
15. We need to **find out** the truth about what happened.
16. Can you **look after** my cat while I'm on vacation?
17. He **finished off** his chores quickly and then went out to play.
18. We have **run out of** milk. Can you buy some on your way home?
19. Please **pass on** this message to the team.
20. It's important to **take care of** the environment for future generations.