The correct answer is D) all of the above. The approved type of gas detecting system on an LNG carrier is required to detect methane leaks in the barrier spaces, boiler burner supply piping, and cargo handling rooms. This is specified in the regulations governing the design and safety requirements for LNG carriers, which fall under the jurisdiction of the US Coast Guard. The gas detection system is a critical safety feature to monitor for potential leaks of the flammable LNG cargo throughout the various spaces on the vessel. The other answer choices are incorrect because they do not encompass all the areas where gas detection is required. Limiting the detection to only one or two of these spaces would not provide the comprehensive monitoring needed for the safe operation of an LNG carrier.