The most appropriate option to fill in the blank is Would.

The sentence is a polite question asking if someone would like some water. The word "would" is used to make a polite request. It is more polite than "do" or "can".

The other options are not as appropriate.

• Do is too informal for a polite request.
• Can is also too informal for a polite request. It can also be used to ask for permission, which is not the case in this sentence.
• Shall is more formal than "would", but it is not as commonly used in everyday speech.