Learn Croatian: Zašto tako glasno slušaš glazbu? Ne čujem tvoj glas! - Why are you listening to music so loudly? I do not hear your voice!

This is a great example of what this lesson is about! Slušati (to listen) and čuti (to hear) act as an aspectual pair, even though they come from completely different roots (a concept called "suppletion"). Just like in English, slušati is the continuous action of paying attention to a sound (imperfective), while čuti is the sudden or completed perception of that sound (perfective).

Both glazbu and tvoj glas are direct objects. Why does glazba change its ending while tvoj glas stays the same?

Both are in the accusative case, but they follow different rules based on their gender. Glazba is a feminine noun, and feminine nouns change their -a ending to -u in the accusative. Glas is a masculine inanimate noun (a non-living thing). Masculine inanimate nouns do not change their endings in the accusative case; they look exactly the same as their basic dictionary form.

I notice that glasno (loudly) and glas (voice) look very similar. Is there a connection?

Yes, they share the exact same root! Glas is the noun for "voice" or "sound." By adding a suffix to it, it becomes the adverb glasno, meaning "loudly." You can think of glasno as doing something "with a big voice."

Why is Ne čujem written as two separate words? I thought is sometimes attached directly to the verb.