Final answer:
The Federal Housing Administration (FHA) and the Home Owners' Loan Corporation (HOLC) are the two agencies recognized for maintaining the racial homogeneity of suburbs post-World War II through practices such as redlining and discriminatory mortgage lending criteria.
Step-by-step explanation:
The two agencies that are viewed as instrumental in keeping the newly developing suburbs after World War II for white people only are the Federal Housing Administration (FHA) and the Home Owners' Loan Corporation (HOLC). The FHA was created as part of Roosevelt's New Deal, intended to boost homeownership by providing federally backed mortgages. However, the FHA's underwriting manual and the criteria for insuring loans favored new suburban home construction and rehabilitation of inner-city homes, leading to a process that incentivized white families to move to the suburbs and inadvertently contributing to segregation due to discriminatory practices like redlining. The HOLC helped in refinancing mortgages to prevent foreclosures and, by doing so, was also linked to discriminatory practices that affected which areas and populations would benefit from these government programs.