What event gave Thorin the confidence that he might be able to defeat the armies of the lake men and elves -hobbit?

Thorin gained confidence in his ability to defeat the armies of the Lake-men and elves after successfully holding off a siege at the Lonely Mountain. He believed that the dwarves' fortified position and their determination to protect their newfound treasure would give them the upper hand. Additionally, the arrival of reinforcements and the fierce loyalty of his kin bolstered his resolve to face the encroaching forces. This combination of strategic advantage and the strength of his allies fueled his confidence in the impending conflict.