Diet Program, Is It Ok?

I started The Carb Cycling Codex Gain muscle and lose fat optimally by Christian Thibaudeau
2 weeks ago.
i build a diet menu but i’m not sure about the numbers.
i give you a little bit information so you can help me.

i’m 5’10 , 211 lbs , age:29 , i think that i have 22% body fat.
i had injury 6 month ago in my left shoulder so i didn’t trained.
now i train 5 times a week each day different muscle .
i don’t do cardio because a knee problem.
and my menu contain
cal - 2200
protein - 250 g
carb - 200 g
fat - 37 g
i reduce the carbs every 3 weeks 20 g less. - is it ok??

my goal is to get to about 12% body fat.
is it possible with the details i wrote here?
i read so much articles on getting lean but i never tried it like this.
how long this cycle supposed to last?? so i can check my self every week…
please help me i know how to gain muscle but i never tried to get lean.