The equation that represents the problem is:
\( x + 129 = 468 \)
This equation states that Cheyenne's brother climbed \( x \) feet, and since Cheyenne climbed 129 feet more than him, we add 129 to his distance climbed to equal 468 feet (the distance Cheyenne climbed).
So, the correct choice from the responses provided is:
x + 129 = 468