For how long does a worker bee live in the summer?

The correct option is For 2 months.

Worker bees have different lifespans depending on the season in which they emerge. During the active summer months, worker bees work exceptionally hard, foraging for nectar and pollen, feeding the brood, producing honey, and guarding the hive.
This intense physical labor and high metabolic activity literally wears out their bodies, resulting in a lifespan of only about 5 to 6 weeks (which falls closest to the 2 months range among the given options).
In contrast, worker bees born in the autumn do not have to forage and can live for up to 6 months to help the colony survive the winter.