I have studied English for 4 months. To study English, I recently started listening to English music. Though I had never really listened to English music until I started studying English, after listening, I began to like it very much . Now whenever I do something to do, I’m listening it. There are some parts of your text that I could not quite understand, so just added a couple grammatical corrections. Here's how I would rewrite it: I have been studying English for 4 months now. As part of my studies, I recently started listening to English music. Even though I had never really listened to English music before, I have come to like it very much. Now, whenever I am doing something, I listen to it.

A more concise way to say this could also be: I have been studying English for four months. To study, I have started listening to music in English. It’s my first listening to music in English and I enjoy it a lot. I like to listen while doing other things.