Final answer:
Prometheus hid the prophecy that one of Zeus' children would overthrow him, which influenced Zeus' actions within the Greek pantheon.
Step-by-step explanation:
The knowledge that Prometheus hid regarding Zeus' future is that there was a prophecy that Zeus would be overthrown by one of his children, just as he had overthrown his own father, Cronus. This secret played a significant role in the dynamics of the Greek pantheon as Zeus took measures to prevent this prophecy from coming to fruition, displaying the themes of fate and power struggles.