G. Prefer and would rather
G1. We can use ‘prefer to (do)’ or ‘prefer -ing’ to say what you prefer in general. I prefer doing something vs. to doing something else. But I prefer to do something vs. rather than (do) something else.
G2. use ‘would prefer to do’ somebody wants in a specific situation (not in general), say ‘would prefer to do something’ (not doing).
G3. Would rather (do) = would prefer (to do). We use would ‘rather + infinitive’ (without to), the negative is ‘I’d rather not (do something) We can say ‘would rather do something than do something else’.
G4. We can say ‘I’d rather you did something’ (not I’d rather you do.) In this structure we use the past (came, did etc.), but the meaning is present not past. I’d rather you didn’t (do something) = I’d prefer you not to do it.