Translation:I like that wine, but not the other.
A Brazilian friend was explaining this to me yesterday that isso & isto are fairly interchangeable as this & that but they always refer to something close to you, aquele/aquela is always that (over there) - ie something far away (this might not be totally true but as I'm struggling with the language in my day to day life, it was a relief to hear)
My earlier studies of the version of this language as spoken in Portugal taught me to exchange the s and the t. So esTe means thiS and esSe means thaT. I have used this rule in every exercise so far and it has always been correct. Obviously it also applies to other forms such as destes and dessas and isto (this) as well as isso (that). A further complication arises with regard to isso however in that in the colloquial or familiar use of Portugal's usage isso can also be this. But if you apply the above approach your answers should be accepted.
Portuguese loves contractions and perhaps the sentence will be less confusing if they are spelled out in full, in which case the sentence is "Eu gosto de esse vinho, mas não de o outro" which is word-for-word: "I like of that wine, but not of the other". The odd thing there is the two uses of "of". It turns out that in Portuguese you don't simply like something you like "of" something so "of" can be ignored, giving: "I like that wine, but not the other". Does that help?
The English transltion is totally unnatural. It should be "...the other ONE". English simply doesn't use adjectives, adverbs and some particles like that. The missing subject has to be replaced by one. "I like this" means "Eu gost desto" = "I like THAT here". While "I like this one" = Eu gosto deste/desta" = I like the ONE here".