The metonymy used in Martin Luther King Jr.'s "I Have a Dream" speech is "the valley" standing in for "the struggles and hardships faced by African Americans."
King uses the phrase "Let freedom ring from the prodigious hilltops of New Hampshire" and then continues with "Let freedom ring from the mighty mountains of New York" before reaching "Let freedom ring from the snow-capped Rockies of Colorado." He builds up to the climax of his speech with a crescendo of "Let freedom ring from every hill and molehill, from every mountainside and valley in the land!"
By using "valley" as a symbol for hardship, King connects the idea of freedom with the overcoming of adversity. He emphasizes the need for freedom to reach every corner of the land, including the places that have historically been associated with suffering and oppression.
This metonymy effectively reinforces the speech's central message of equality and freedom, emphasizing the need for change to encompass all aspects of American life.
