1. I like listening to music programs, both classical and pop.
我喜欢听音乐节目，古典和流行的都喜欢听。
还能这样说：
I enjoy listning to music programs, both classical and pop.
I am fond of listening to music programs, both classical and pop.
应用解析：
on the listen 注意地听着；
listen for 倾耳听，等着听；
listen in 收听（偷听）
2. Open the radio, and let's listen to some music.
打开收音机，咱们听听音乐吧。
还能这样说：
Let's listen to some music on the radio.
We can turn on the radio and listen to music.
谚语：
Better an open enemy than a false friend.
公开的敌人胜于虚假的朋友。
3. I'm no judge of music, but I have my taste.
对音乐我是外行，不过我有自己喜好的音乐。
还能这样说：
I'm a layman in music, but I still have my favor.
I'm strange at music, but I know what I like.
应用解析：
judge from the fact 根据事实推测；
judge between right and wrong 判断是非；
so far as I can judge 据我判断，我认为；
judging from 根据……来判断
4. I like working to music.
我喜欢一边工作一边听音乐。
还能这样说：
I like to listen to music as I work.
I am fond of listening to music when I am busy working.
谚语：
All work and no play make Jack a dull boy.
只工作，不玩耍，聪明的孩子也变傻。