If you really want to know the reason, it's a gender thing. Tafarn is feminine and feminine nouns mutate after the definite article ("y" or "'r").
Banc is masculine, and doesn't mutate after the definite article.
However, in a way, knowing this isn't going to help you much in speaking. (It might help you in writing, when you have time to think about things and look them up). If you have to stop and ask yourself what gender a word is before you speak, the conversation will have moved on, and you won't get a word out.
And this is why SSiW is superior to most other courses (probably including Duolngo), because we just learn things like this in spoken phrases, naturally, much as a child learns its 1st language.
I think some SSiW lessons / challenges do touch on grammar indirectly, but generally, we "paid a phoeni" about grammar. There will be time to learn a bit of grammar (if you want to), when you've got all the courses / levels behind you.
There is however, one handy piece of "grammar" that you can use as a rule of thumb for mutations, not in the situation that you describe, but in another one that comes up frequently:
If the word that comes after the subject of a sentence begins with one of the mutatable letters, then it mutates. This is why "mynd" mutates to "fynd" in "(w)nes i fynd". (Note that it's not just because it's "i", because it also mutates in "(w)nes ti fynd".
(This "rule" is courtesy of Gareth King).