At the weight you were when this A1C blood test was taken indicates you were eating some type of carbs that could have resulted in that level. Maybe not sugar, maybe whole grain breads and beer? As diedra explained, it indicates an average of BG readings over roughly the previous 3 month period, but the rate of red blood cell turnover can vary.

From your previous posts, it seemed that you had not started LC when the test was taken and BG can respond quickly, so 12.4 is likely accurate. Even if it wasn't, I would suggest that you stick to a VLC diet for about four months, and then request a A1C again. You are not going to get any information from it that should change your course of action now. Believe Ken had a similar situation, he had been eating LC for five weeks before the A1C test was taken. The A1C was still high while the BG was already in normal ranges. Rather than prescribe meds, his doctor had him continue with what he was eating.
Eat a strict LC diet, and use that glucose meter often to test your reaction to foods. By the end of 4 months, you will have a better idea what LC foods work well for you and which to avoid.