"I like my coffee strong."
Translation:J'aime mon café fort.
"I like my strong coffee" (which usually means "I like the coffee I have, which so happens to be strong, and perhaps even because it's strong.") is different from "I like my coffee strong" (which is a way of saying "I like it when my coffee is strong.") But this implies that French is the same, doesn't it? Is this going to be purely context then, e.g. it's more likely to be the latter if, say, there's no coffee present? Could you avoid ambiguity by saying something like «Je l'aime quand mon café est fort»?
The possesive (mon,ma) you use depends on the word it's in relation to. So like alvaro said, since in this case coffee is masculine (meaning you would say «le café»), you would use «mon». If the word was feminine however, like «la robe» or «la femme», you would use «ma». So basically, mon is masculine and ma is feminine.
«Aimer» can be combined with various adverbs for nuance, e.g. «aimer bien» or «aimer beaucoup». «Aimer bien» in particular is usually just translated as "like" since it's a generic "like" that keeps «aimer» from meaning "love" (not that it would mean love in this context anyway). It also accepts plain old «aimer».
Previously duo didn't use 'J'aime bien' in the context of liking something, but doesn't the exclusion of 'bien' mean love? So shouldn't all of the examples before have used "J'aime bien (du café)" instead of just "J'aime (du café)?" Is this a rule (saying "J'aime bien") that should be followed from now on out when meaning 'like' and not 'love?' Or can you get away not specifying when talking about an item?