もしよろしければホテルを予約してあげましょうか？って英語でなんて言うの？

The first example uses the modal(helping verb) shall with the main verb book creating verb phrase shall I book. Simple way to ask a polite question Example two is similar with modal (helping verb) would and main verb like used to form question would you like. Both are good ways of forming a question in a polite manner

In the first sentence you are offering to make the arrangements for your visiting friend. In the second sentence, you are enquiring whether youir friend prefers to make the arrangements themself or let you do it for them? In these days of online booking, most people would probably like to select a place themselves and perhaps check with you after they made a choice as to the suitability of their selection.

Both of these phrases will let the person you are talking to that you are wondering about their accommodation. The first one you are first asking if they already have a room? If not, would they like you to book one for them. The second one you have already assumed that they don't have a room yet and are asking if you can book them one.

"Would you like?" is a polite way to ask if the person would appreciate something. Assistance is a word for help that is given or received. Book a hotel, make a reservation, and reserve a hotel room all refer to ways of arranging to have a hotel room for use at a later time.

If you are referring to a hotel room then you can also use the term 'room' if you say 'would you like me to?' you are asking if someone wants you to do something for them you can also say 'shall I' To make a reservation or to reserve something is the same as to 'book' it

Native speakers will say like this: “I can book a hotel room for you if you want me to”. There are lots of other ways to say it, but this one is the most accurate and most commonly used. Here is an example on how to use this in a conversation: A: I'll be visiting Japan soon! B: Awesome! I can book a hotel room for you if you want me to.

There are many ways you can ask this, but the most common is "Would you like me to book you a hotel room?" This simply asks for permission for you to purchase a hotel room for the person, and it is a formal question. If you want to offer to do it, then you can say, "I can book you a hotel room if you want." This is a polite way of saying you will do it, while expecting his/her opinion. Another polite way to offer is by saying, "Just let me know if you would ever like for me to book you a hotel room." This gives them time to think about it and tell you their decision later.