"Громкую музыку" is the accusative form, since "Loud music" is the direct object, the noun and its adjective have to take the accusative form.
Adjectives decline differently than nouns.
"Громкую" is the feminine accusative form. "Громку" isn't any form.
It's obvious you're right, so this is a complaint about Duo, not about you:
Duo's Tips say that the accusative is the same as the nominative declension of adjectives. Obviously, this is wrong. Or it's only partly right, with the other part left out of the tips.
From Duo Tips, accusative:
'Neuter nouns and feminine nouns with a final -ь (e.g., «мы́шь») use the Nominative form'
feminine nouns ending in -а / -я have a separate form -а/-я > -у/-ю
громкая (-ая) > громкую
I don't know if it's relevant to Russian, but there's a difference between "not like" and "dislike". I can not like something by being indifferent to it - I don't know about something, so I don't like it and I don't dislike it. If I dislike something, it means I have a definite negative opinion about something. The two things are not the same, although people often use the two verbs as synonyms.
Are the double sounds pronounced or just written? I mean, I hear 'gromku' as in громку and not 'grómkuyu' or similar. Same for ая ending or the even more confusing яя. Are they 'aya' and 'yaya' respectively?
Громкую is pronounced with an "oo-yoo" sound at the end - see here. I don't think that the яя has a yaya sound - see here or here. Instead, I regard it more as a "yuh-yuh" sound - see rules for vowel reduction here, which indicates that after the stress, the я takes what that page describes in section 6.3 as a "yuh" sound, or an apostrophized schwa. (I may have made up the word "apostrophized." Sorry.) Since both я's are after the stressed vowel, they are both reduced.
I do not think the Duolingo audio is fantastic on pronouncing this particular instance of громкую.
I can't copy and paste texts here on Duolingo, but you can read StevenSambora's comment.
I thought "do not like..." should be не нравится..., whereras не любите is unnatrual, as a Dler pointed out in a relevant discussion.
Me too. I had to choose from given words so I had no choice but when this sentence comes up again, i am sure to make this exact mistake. Can anyone point out to me why не нравится is wrong here?
Mainly, "любит" means "he/she loves" only when the object is a person; otherwise (as here) it means "he/she likes." https://www.duolingo.com/skill/ru/Infinitive%2C-Likes-and-Dislikes
I'm not sure about "Mum." Here's the course policy: https://www.duolingo.com/skill/ru/Basics-1 "Just to make it clear, we are using American English in this course—but don't worry, we will accept all versions of English where appropriate. Just be careful around expressions like 'bathroom' or '1st floor', because these may mean different things than what you are used to." (Dinner/supper is a big one.)
I don't know how to make an accusative form from adjectives somebody please help me.
My friend, try this site - it will help you see the patterns of the endings: http://www.russianlessons.net/grammar/adjectives.php
I always also recommend this site: en.OpenRussian.org - since it is an online, searchable dictionary that has (just about every) adjective you can think of, as well as all the declensions.