My sister was/is like that. If she can hear the music, she can play it (piano). She's also so good at languages that she taught both German and French at the middle school and high school levels, and still speaks both fluently. She still does interpretation for companies and the local po-po where she lives.
She still doesn't read music, despite having taken violin lessons.
If I hear something enough times, I can replicate it. I can read music, and when I was younger, could remember everything I read, nearly verbatim. At my age, not so much.
For writers, I always offer 2 bits of advice. 1st, you have to read. Voraciously. It's a must. You also need to develop, if you don't have it already, the ability to immerse yourself in what you read. You need to literally "hear" the voices of the characters you encounter. Good authors make it easy. Others make you work at it.
2nd, you need to read your work out loud. Sure, you can "hear" with your inner ear your own voice, but you're too close to it. It's important to set the work aside and come back to it fresh, and be able to hear what it sounds like out loud.
There are other tips and strategies for becoming a good writer, but the ability to "hear" also relates to music, and probably to math, but I've never figured that part out. I suck at math, even though it's just another language like music or English, French, German, and so on.
