Теория:

Study the information about prefer and would rather.
  
1. You can use prefer to and prefer -ing to say what you prefer in general.

I don’t like countries. I prefer to live in cities/I prefer living in cities.
  
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Remember the structures!
 

I prefer something to something else.

I prefer doing something to doing something else.

I prefer to do something rather than (do) something else.
 
I prefer to drive a car than travel by train.
  
2. Would prefer (I’d prefer)

This phrase can be used when you say what somebody wants in a specific situation.

Would you prefer espresso or cappuccino?
  
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3. Would rather = would prefer

We should use would rather + infinitive (without to)

I’d rather stay at home today.
 
4. The structure: I’d rather you did something.

In this case we use the past, but the meaning is present.

I’d rather you made lunch.

I’d rather make lunch.
  
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I’d rather you didn’t do something = I’d prefer you not to do it.

I’d rather you didn’t tell anyone about these details.
Источники:
www.politico.com
theodysseyonline.com
www.whitegullinn.com