Final answer:
Bard knew to aim for the hollow of Smaug's left breast based on the information he had gathered.
Step-by-step explanation:
When Bard was aiming his black arrow at Smaug, he knew he should aim for the hollow of Smaug's left breast based on the information he had gathered. Bard had learned from the thrush that the only place where Smaug had a weak spot in his armor was in the hollow of his left breast. This knowledge allowed Bard to effectively target that specific area to have a chance at slaying the dragon.