Which act allows federal funding for an educational institution to be cut if that institution prohibits military recruiting or ROTC?

The Solomon Act is the piece of legislation that stipulates that educational institutions risk losing federal funding if they have policies that prohibit military recruitment and the operation of the Reserve Officers' Training Corps (ROTC) on their campuses. The act was enacted to ensure that military recruiters have the same access to students as other employers. This was a response to universities adopting policies aimed at restricting military presence due to various social and political concerns. The Solomon Act enforces the idea that federal funding should only go to institutions that accept and provide equal access for military representatives.

In the context of the other options, the Federal Financial Assistance Act pertains to the provision of federal aid to students but does not specifically address military recruitment. The Patriot Act focuses on national security and law enforcement in the context of terrorism, while Executive Order 12372 relates to intergovernmental review of federal programs and does not have any direct connection to military recruitment or the ROTC. Thus, the Solomon Act is uniquely positioned as the correct answer in this context.