- For Teachers
I would like to have some coffee.
I would like some tea.
Here the 'woulds' above indicates politeness.
They are not related to subjunctive mood, because the statements are factual.
I would prefer you not to smoke.
I would prefer that you did not smoke.
I would rather you did not smoke.
All the 3 sentences above are non-factual.
The "woulds" above are used to indicate subjunctive mood, also as you can see from the past subjunctive of "do".
Do you have any ideas?