Translation:My grandfather likes listening to Italian music.
My answer of "My grandpa likes to listen to Italian music" was accepted today (20 June, 2018). I wonder if you didn't have something else wrong in your answer. Also, be careful of the suggestions/corrections displayed on the page where you get it wrong. Depending on the mistake that was made, it can give you some misleading advice. The translation on the discussion page is the one I always take as the "official" answer.
I wonder...why does it have to be "le" there? How do I know when and where to use it?
In this case, the 'le' means to him. the literal translation of gustar is "to be pleasing". By putting le in there, we make it "is pleasing to him", but in English, we equate it to "to like". Without the le, the sentence would translate to "My grandfather is pleasing to listen to Italian music." This gets extremely awkward when the sentence is "My grandfather likes kids." and it is translated wrong. "A mi abuelo gusta los niños" translates to (roughly) "My grandfather is pleasing the kids." (The silly examples are what helped me to remember this stuff even years later.) I hope this helps!
A few other verbs that require the (me, te, le, nos, les) are: faltar, encantar, importar, hacer falta, parecer, picar. You can look up the definitions of any of the words you do not know.
Source: I studied Spanish in school for ~10 years.
Fantastic explanation, I think I will be able to memorize it from now on. Btw, could you also tell why we put 'A' at the beginning? I was going through the directory when suddenly an A is given at the beginning of such sentences and I fail to grasp the concept when it is needed and when the subject of the sentence can go without an 'A' at the beginning.
The a at the beginning clarifies who likes it. It's used mostly with le (and les) because le just by itself could mean he/she/it or even you as in usted. For example, a él le gusta means "he likes it."
It also appears redundantly with me/te/nos as a mí /ti/nosotros for emphasis, usually in response to a question.
"my grandpa likes to hear italian music"
why does duolingo not accept this?
Well, hearing music is an involuntary thing that doesn't require any attention---whereas listening to music is intentional and usually purposeful.
This distinction also exists in the Spanish verbs escuchar and oír.
Why not "la mucisa italiana"? I thought when referring to something in general we use the definite article.
Normally that is the case, especially with backward verbs like gustar where música italiana appears to be the subject.
However, upon closer inspection, the subject is technically escuchar música italiana---and música is the object of a preposition (an implied one, listening to), where the rule regarding definite articles for generalities is actually the opposite.
That is also what I wrote and it was marked wrong. Please someone tell us why it is the incorrect answer.