Based on the binomial classification system, the mosquito, anopheles punctulatus, is most closely related in structure to culex pipens, anopheles quadrimaculatus, ades aeqypti, or aedes sollicitans?

The answer is Anopheles quadrimaculatus.

According to binomial nomenclature, a formal system of naming species, a name of species is composed of two parts. The first word indicates the organism's genus classification, the second word indicates the species within a genus. In taxonomy hierarchy, the genus is above species. So, species with the same first name belong to the same genus, which means they are closely related. Anopheles punctulatus is closely related to Anopheles quadrimaculatus, which  is concluded from the same first name, the name of the genus - Anopheles.