Translation:She is a composer and she has a lot of good music.
Could this mean both of: she owns good music, and has written good music?
Does music end in an a because it is plural? Also, is music in the nominative case? I cannot figure out why the -ей ending is on the root adj form хорош-. What case is the adjective in? Even though the base nominative form of the adjective good is хороший (a "hard" adjective), it appears to follow the pattern of soft adjectives by taking the -ей ending.
Hope you get a more authoritative source, maybe a link. But:
много here is causing "хорошая музыка" to be in the genitive case, "хорошей музыки". "a lot OF something". Since к, х, ш, щ, ч, ж will never be followed by ы but instead и you get музыки. Remembering 'music' is feminine, we know that 'good' has to be made feminine too. Genitive case feminine adjectives usually end ой, with the soft ones ей, like you said.
I'm not sure, but it seems like a similar but different spelling rule operates so that adjectives with ш, ч, ж get some of the same endings as soft adjectives but not all. While adjectives with к, х get regular hard adjective endings except that where a ы would normally occur there is и instead.
Contrast nominative soft синяя versus горячая хорошая свежая, accusitive soft синюю versus горячую хорошую свежую. But then compare the prepositional, genitive, and dative forms of these four, all ей versus hard ой. For forms like новой and хорошей the difference between the pronunciation of the ending should really be slight since in both instances the stress is not on the ending and o and e are a stressed/unstressed pair in Russian. The difference is spelling convention.
большой though has competing influences because it has ш, ч, ж, on the one hand, but end stress on the other hand. It gets the stressed о version of е for all those endings where синий, горячий, хороший, свежий agree with eachother in having е.
Notice however that all the hard consonants ш, ч, ж and including к, х still cannot be followed by ы in adjectives no matter where the stress lies. Thus новые, новых, but большие, больших. So the situation is more complex than just hard/soft I think.
Now I'll have to follow this and edit/delete if this gets superseded.
"She is a composer and has a lot of good music" is also correct and the more proper sentence.
agree with a couple of comments on here about "she is a composer and has a lot of good music" being an OK phrase here, and I could not help to have a slight smile when Duo said "you have used the wrong word" and then placed the phrase "She is a composer and she's a lot of good music" where "she's" is "she is" but I guess at a stretch it could be "she has" but to my ear, that sounds a bit off. But all good, This course is incredibly valuable and even surpasses many (may I even say ALL) of the paid courses that I have seen to date. Keep up the good work Duo ))) And thank you ))