How many weeks or months do I have to fast to lose weight around 12 kg ?

Fasting doesn't help you lose weight. Eat properly and you will lose weight. Only vegetables, fruit, dairy, meat, and grains. No junk food and fast food at all!!!
Additionally you need to exercise to lose weight even faster.
Try this: make your self a day-1, day-2 schedule.
Day-1, do a full body workout (with free weights, don't use machines).
Day-2, do only cardio (running and sprinting, or you decide)
So to start, use this schedule 4 days a week. So, Monday=cardio, Tuesday=weights, Wednesday=cardio, Thursday=weights. Then advance to 6 days a week.

I guarantee you will lose at least 30-40 pounds in 1-2 months, with what I told you.
If you like your results and want to start building muscle, eat 1 gram of protein for every pound of body mass, every day.
Believe me this will work, I've done it.