p would be the average of the bounds, or (12.6%+24.4%)/2 = 37%/2 = 18.5%
The margin of error will be the value between either bound and p, so you can do 24.4%-18.5%=5.9% or 18.5%-12.6%=5.9%
Thus, the confidence interval can be written as p±ME = 18.5% ± 5.9% = 0.185 ± 0.059
Hope this helped!