Following most reputable diets (low-carb, paleo, intermittent fasting, the zone etc.) you can expect to lose up to 1% bodyfat per week as a rough yardstick. Overweight individuals can expect to lose a bit more than this, and as you get leaner progress may slow down, but a rough ballpark would be 12 weeks.
Fat loss is not always linear though, and you may notice some weeks you make great progress and other weeks it may feel like you’re getting stagnant. Keep your diet tight, incrementally ratchet up your activity, and you should be there in 2-3 months easy.
In general, you can lose 1-2 lbs of mostly fat per week by maintaining a 500-1000 calorie deficit per day. At higher body fat percentages, such as those about 15%, you will probably be able to lose fat versus lean body mass (muscle) at a ratio highly favorable to losing fat (close to 100% fat loss). As you get to lower body fats, you might need to slow down weight loss per week in order to preserve as much lean body mass as possible. Otherwise, you’ll lose weight, but a good chunk of that weight lost becomes muscle lost, which would consequently dampen how fit you look despite fat loss.
Once you get to 12-13% BF, you will have to keep your diet very strict, and from that point on, you should probably expect a good 4-6 weeks before reaching 10%.
Before that, from 21 to 14% BF, you could achieve that in around 8 weeks. This would be if you’re maintaining at least a 500 calorie deficit each day.
In summary, probably at least 3 months if you never fall off the wagon with your diet or training regime. More realistic estimate would probably put you at around 4 to 7 months if you end up screwing up couple times a month.