'Close' and 'Shut' are words that are frequently confused and used in the wrong situations.

There are occasions when they could be used within the same sentence, such as

Close/shut the window!

The restaurant shuts/closes at 10pm.

Close/Shut your mouth!

The past participles closed/shut can also be used in a similar way, when  used as adjectives.

The window is closed/shut

The restaurant shut/closed at 10pm yesterday.

You closed/shut your mouth.

When placed before a noun - closed is used, not shut.

A Closed window.

A Closed mouth.

If you are referring to slow movements close is preferred, a shut is more of a command.

The flowers close for the night.

He closed his eyes in thought.

She shut the book for the final time.

Compared to:

Shut your eyes now!

Shut your book and listen to me!

We also close things when they come to an end.

Close a letter

Close a road

Close the railway

Close a bank account

Bring the meeting to a close

Close the communication link

Close the house up for the summer

 

Answer:  shut (a) your book and listen to me!

This answer is correct because the exclamation mark at the end of the sentence makes it something that has to be done now.  If there was no exclamation mark, close would be the best option.