聞く and 聞こえる: listen, ask, or hear naturally
Compare deliberate listening and asking with a sound that reaches your ears. Also distinguish 聞こえる from the potential form 聞ける.
聞く: listen or ask
聞く can describe deliberately listening to a sound. 毎晩、音楽を聞きます。 The music is the object selected for listening, so it takes を.
聞く can also mean asking someone for information. 先生に言葉の意味を聞きました。 Here, 先生に marks the person asked, and 言葉の意味を marks what was asked about. Do not restrict 聞く to receiving sounds.
聞こえる: a sound reaches you
聞こえる describes a sound being audible even without a deliberate effort to listen. 外から鳥の声が聞こえます。 The sound that can be heard, 鳥の声, takes が.
声が小さくてよく聞こえません。 says that the voice is too quiet to hear well. The focus is whether the sound reaches the listener, so this pattern should not simply be exchanged with 音楽を聞く.
聞ける: be able to perform 聞く
聞ける is the potential form of 聞く. このアプリなら外国のラジオが聞けます。 says that the app makes it possible to listen to foreign radio. 授業のあとで先生に聞けます。 says that there will be an opportunity to ask the teacher after class.
聞こえる presents a naturally audible state, while 聞ける presents conditions that allow the intentional action 聞く. Both may be translated as “can hear” in English, so check whether intention, an opportunity, or simple audibility is involved.
Quick check: Does 隣の部屋から音楽が聞こえます mean that someone deliberately chose to listen to the music?
Show the answer and why
No. It says that music can naturally be heard from the next room. Deliberately listening to it would be expressed with a pattern such as 音楽を聞きます.