Many years ago, around 15 or a little bit more, I practised karate. I was a child and reached 9th kyu. Now I want to come back to the karate.
Should I start from 9th kyu or I should start from the beginning?
Your kyu rank is relative to the style (and dojo) that you practiced at when you were 15. Realistically, no matter what the style 9th kyu is barely more than beginner.
I'd suggest you start again from white belt (whatever kyu that happens to be in the dojo you'll be attending). If you remember stuff then you should be able to advance fairly quickly. I've trained at other dojos as a white belt even once I had my black, it can be enlightening getting back in at that level.
Firstly, whatever you learned fifteen years ago might be muddled by age and memory lose. I would not rely on it. Secondly, since it was a child's rank and not adult, the syllabus might have been radically different. Finally, after any long break period, it is advisable to start again as a beginner. If it all comes back, you can wear your old coloured belt. If it all comes back, any good teacher should see it and promote you to where they think you should be. Besides, whatever your belt colour is matter less than what you know.
Start from the beginning again and enjoy the journey.
In addition to the points made above, as someone who has found himself in this situation before, your teachers may decide to promote you more than one rank at a time (less of an issue at 9th kyu, but something to keep in mind). In that situation, I'd advise pushing back if they try to charge you multiples of the testing fee. The purpose of testing fees is to cover expenses, and testing you once to advance you three belts doesn't cost any more than testing you once to advance one belt. This is especially the case if you don't receive the intermediate belts (something I've occasionally rued with a bit of humor, as one of the Tae Kwan Do schools I was fastracked in had the famed "camo belt", although I know I could readily enough just buy one of my own).