Final answer:
The Fair Housing Act of 1968 is the law that prohibits all racial discrimination in the sale or rental of publicly or privately held property.
Step-by-step explanation:
The law that prohibits all racial discrimination in the sale or rental of publicly or privately held property, without exception, is the Fair Housing Act of 1968 (also known as the Civil Rights Act of 1968). This act was implemented to address and eliminate housing discrimination based on race, color, religion, or national origin. It ensures that everyone has equal opportunities to purchase or rent properties, regardless of their racial background.