Final answer:
Martin Luther King Jr. compared the African American struggle for equality to a promise of equality similar to a bounced check, indicating that America had failed to fulfill its promises to African Americans.
Step-by-step explanation:
The comparison King made between the African American struggle for equality and cashing a check is best described as the promise of equality being like a bounced check. This metaphor was used to illustrate how the historical promises of freedom and equality to African Americans were not being honored, akin to a check that comes back marked 'insufficient funds'.
However, King conveyed his belief that the bank of justice was not bankrupt and that America had the means to fulfill these promises. Hence, the correct answer to the question is: B) The promise of equality was like a bounced check.