Do I really hear N instead of M at the beginning?
The audio sounds fine.
ye it sounds like that but it shouldn't; it's still M
How do you say "don't like" sth.?
You put "nie" before the verb, and the object takes Genitive instead of Accusative. "Mężczyzna nie lubi wina".
Only Accusative changes the case when negated, other cases stay unchanged.
I am assuming wino has no accusative ending, so it's just "wino" not "winę"?
"wino" is neuter, so its Accusative is identical to Nominative.
"winę" is Accusative of "wina", which is "guilt".
"wina" is also Nominative plural and Accusative plural "wines", but that's aside.