Final answer:
To achieve an abdominal radiograph with half the density, you should decrease the mAs by half to 6 mAs while keeping the kVp the same.
Step-by-step explanation:
To produce an abdominal radiograph with half the density of the original image, which required a technique of 12 milliampere-seconds (mAs) at 68 kilovolts peak (kVp) and turned out too dark, you would need to decrease the milliampere-seconds (mAs) since it is directly proportional to the density of the x-ray image. Specifically, you would decrease the mAs by one-half to achieve one-half the density. Therefore, using 6 mAs while maintaining the 68 kVp would be the appropriate technique. It is important to be mindful of the radiation doses associated with x-ray procedures, as medical doses are generally kept low, and diagnostic radiation is used when the benefit justifies the risk.