Final answer:
Martin Luther King Jr. was engaging in a metaphor when he likened the civil rights struggle to cashing a "check" at the "bank" of American Justice.
Step-by-step explanation:
When Martin Luther King Jr. likened the civil rights struggle to cashing a "check" at the "bank" of American Justice, he was engaging in a metaphor. A metaphor is a figure of speech that compares two unrelated things for rhetorical effect. In this case, King compared the civil rights struggle to the act of cashing a check to emphasize the idea of African Americans demanding equality and justice that they were promised but had not yet received.