Final answer:
The Economic Opportunity Act of 1964 was the main offensive in Lyndon Johnson's war on poverty and the cornerstone of his Great Society program, focusing on antipoverty measures, job training, and educational support.
Step-by-step explanation:
The law that was the main offensive in Lyndon Johnson's "war on poverty" and the cornerstone of his Great Society program was the Economic Opportunity Act (EOA) of 1964. This act was a significant step towards Johnson's goal to eradicate poverty in the United States, by allocating almost $1 billion for antipoverty measures that included job training, youth programs, and small business loans. The legislation also established initiatives like the Volunteers in Service to America (VISTA), the Job Corps, and Project Head Start, which provided educational support for underprivileged pre-school children.