Name one of the two labors that didn't count for Heracles.

Heracles undertook twelve labors as penance, but two of those labors did not count toward his overall total due to specific reasons. The labor of killing the Hydra is one of those. When Heracles killed the Hydra, he received assistance from his nephew Iolaus, who helped him by cauterizing the stumps of the heads to prevent them from regenerating. This external help played a significant role in the completion of the task, and thus Hera, who was overseeing the labors, argued that the labor should not count since it could not be considered entirely his own achievement.

In contrast, tasks such as slaying the Nemean Lion and capturing the Golden Hind were completed solely by Heracles, showcasing his strength and skill without external assistance. The cleaning of the Augean stables, while also a labor that faced unique challenges, still counted towards his total because he ultimately accomplished it through his ingenuity and effort without external help. Therefore, the labor of killing the Hydra was deemed invalid in the context of Heracles' total labors due to the significant assistance and intervention involved.