Final answer:
The intended audience is best represented by the phrase where the speaker asks every man present to be a role model for the younger generation, highlighting the responsibility of adults.
Step-by-step explanation:
The phrase from the quotation that best shows the intended audience is "I ask that every man here constitute himself his brother's keeper by setting an example to that younger brother which will prevent him from getting such a false estimate of life." This phrase directly addresses the listeners ('every man here') and assigns them the responsibility of becoming role models for the 'younger brother', which illustrates that the speaker is primarily talking to an audience of adults with the intent of influencing their behavior towards the younger generation.