Final answer:
It is unclear when Franklin heard Increase Mather preach based on the available information.
Step-by-step explanation:
Based on the information provided, it is unclear when Franklin heard Increase Mather preach. The available sources mention Franklin's involvement in establishing reading libraries, founding a philosophical society, and supporting philanthropic projects. However, there is no specific mention of Franklin hearing Mather preach. Therefore, we cannot determine the exact time when this event occurred.