You can write this sentence two ways. Here we have to use 좋다 because 저 has the topic particle and 학생 has the subject particle. "As for me, the busy student is good" which in English we just translate to "like" anyway.
If you wanted to use 좋아하다 you have to change the particles. 제가 바쁜 학생을 정말 좋아합니다. When you like something, that thing receives the object particle.
Another awkward English sentence. Duo, your Korean section is kind of disappointing.
The tool flagged "a busy student" as wrong (given answer is "the busy student"). Again, can't Duolingo globally recognise "a/an" = "the" = ignore?