How do you fix the problem of ac blowing through back vents but not through the front vents?

After Unplugging your ac check the opening of the front with something that you can slide inside the opening like a tooth brush. Do it gently.

There is a blower behind the opening. At times a lot of dust particles get stuck in the blower ( its like a long roller ). All you have to do is clean this blower with the brush.

If you could post the brand of your Ac, Type and capacity, It will be more helpful.

Generally its not difficult after you have seen it being done once.

Tell me if it works.