Final answer:
The method not used by governments to provide attorneys for indigent defendants is retained counsel, since it involves private attorneys hired directly by individuals.
Step-by-step explanation:
The correct answer to which method is not one of the three main methods that governments use to provide attorneys for indigent criminal defendants is: a) retained counsel. The three main methods recognized for providing legal representation to indigent defendants are: b) public defender programs, c) assigned counsel, and d) contract attorney systems. Retained counsel refers to private attorneys that individuals hire and pay for, which is not a method employed by the government to provide legal representation to those who cannot afford it.