I. 1. turn down

   2. compare

   3. Relations

   4. to swim

   5. communication

   6. successfully

II. 1. (to) work out

    2. is quite popular with

    3. proper; to

    4. though / although

    5. cut out

    6. explain; to

III. One possible version:

Dear Daming,

I know your problem. You’ve really made mistakes. Firstly, you used your classmate’s pen without her permission. Secondly, when you broke the pen, you didn’t tell her the truth.

In my opinion, you should first say sorry to her for what you did.Then you should offer to pay for the pen. You can buy a new one for her with your pocket money. She will realize that your truly sorry.

I hope the advice can help you. I’m sure you will get on well with her soon.

Yours,

Tom