The question is asking about the function of the underlined word 'can' in the sentence, 'Can you open the window, please? It is extremely hot in this room.' Let's examine the options to determine the correct answer:
A. Express someone's skill or ability : This option is not correct because the word 'can' is not showing someone's skill or ability, but rather asking someone to do something.
B. Request to another person to do something : This is the correct option. The word 'can' is being used to make a polite request for someone to open the window.
C. Ask for permission : This option is not correct because the word 'can' is not about seeking permission in this context; it is requesting action.
D. Offer something to a person : This option is not correct because the sentence is not offering anything to someone.
Therefore, the function of the underlined word 'can' in this context is to request to another person to do something , which corresponds to option B.