Which insect may build up in large numbers in basements during periods of dry weather?

The option that indicates millipedes is the correct answer because these insects are commonly known to seek shelter in moist environments and can often be found in large numbers in basements, particularly during dry weather conditions. When their natural habitats become desiccated, millipedes can migrate indoors in search of moisture, making basements an attractive refuge.

Centipedes, while they may occasionally be found in basements, tend to be more solitary and do not typically build up in large numbers. They are predatory insects and more often reside in areas where they can find prey rather than in large groups. The western conifer seed bug, on the other hand, is more associated with specific habitats related to coniferous trees and does not typically invade basements in significant numbers. Box elder bugs are often found outside, especially near box elder trees, and while they do enter homes, they do not accumulate in basements during dry spells to the extent that millipedes do.

This understanding of the behavior and habitat preferences of these insects highlights why millipedes are the most likely to be found in large numbers in basements during dry weather.