There's no specific answer given in the movie about how Red knew where to find the box. It's left as a bit of a mystery, intended to highlight a few things:
* Red's intuition and understanding of Andy: Throughout the film, Red demonstrates an uncanny ability to understand people, particularly Andy. This is shown in many ways, like correctly predicting Andy's escape plan and understanding his quiet determination. His intuition likely led him to believe the box would be where it was.
* Andy's trust in Red: While Andy never explicitly told Red about the box, he likely trusted Red enough to know he'd find it if needed. This trust is a cornerstone of their friendship.
* The power of hope: The box itself represents the hope that Andy held onto throughout his imprisonment. The film's message is that hope can lead you through the darkest of times, and it seems that Andy's hope was strong enough to guide Red to the box, even without direct instructions.
Ultimately, the mystery of the box's location is less about the specifics and more about the emotional impact of the scene. It highlights the deep bond between Red and Andy, the power of trust and hope, and the enduring impact that one person can have on another.