An important technique that provide insight into interesting genetic questions at the molecular level, such as reasons for hairless dogs, is called

DNA sequencing

Explanation:

DNA sequencing is a technique which helps in determining the DNA sequence of any organism. In the human genome project, all the bases that make DNA in humans are sequenced which helped doctors to determine the cause of many genetic diseases and also their treatment.

Hairlessness in dogs can be genetic and the mutated gene can be determined by sequencing the DNA of hairless dog and comparing it with the normal DNA sequence of dog. Therefore the correct answer is DNA sequencing.