Like indicates a desire to do something; prefer indicates a desire to do something over something else.
So:
I would like to discuss the matter in private.
means that I want to discuss the matter in private, but:
I would prefer to discuss the matter in private.
might mean that I would rather discuss the matter privately rather than publicly.
In short, if you and I needed to discuss something, and I wanted to do so privately, I might say to you:
I would like to discuss this matter in private.
However, for the sake of discussion, let's assume I only said,
I would like to discuss this matter with you.
and we were within earshot of other people. You might respond with,
Okay, let's talk about it.
in which case I might reply:
I would prefer to discuss the matter with you in private.
This nuance can be found in the dictionary. NOAD defines the verb like as:
wish for; want
while prefer is defined as:
like (one thing or person) better than another or others (emphasis added)
"I would prefer to discuss the matter in private…" clearly implies there is a choice, as for instance to discuss the matter in public.
Other constructions include "I will discuss the matter only in private…" and "I will not discuss the matter in public…"
Do all those options make sense, both in grammar and logic?
– Robbie Goodwin Jun 14 '20 at 22:10