Translation:I like to work and study.
I don't like this sentence because it uses と for "and" (meaning that the only things the speaker likes are work and study). While it's technically correct, I feel like it develops a bad intuition towards と by making it directly analogous to the English "and" without any sense of exclusivity.
Edit: the alternative particle for "and" I'd use in this case is や, meaning "work and study [and maybe other things too]"
The sound doesn't play on my computer but this is the usual answer to this question:
The g* sounds in Japanese are often nasalised, making it more like a "ng" sound. Lots of languages don't have this sound for the first consonant of a syllable so those languages' speakers often mishear it as "m" instead when it turns up.
If you listen again, can you hear "nga suki desu"?
I don't know if it accepts now, but my guess as to why it's wrong is that "working" and "studying" are verbs turned into nouns (gerunds), while the words used are straight nouns and not gerunds. The Japanese equivalent of that sentence might be more like "私は働くことと勉強することが大好きです。"
i just looked it up in 辞書、and i found out that 仕事 is a する verb. so yeah 仕事する is a thing. and i suppose 働きながら勉強する could be used, but i think 働く is more vague, it could be used for other things other than working at a job, while 仕事する is more for working your job. (I'd look it up in 辞書 so you can see what I'm talking about)