The correct answer is A) New Hampshire Primary.
The significant event that pushed President Johnson to refuse reelection in the 1968 election was the New Hampshire Primary.
The New Hampshire Primary of March 12, 1968, was the moment when President Johnson had to admit that he was not running for the second period of the U.S. presidency. His popularity had considerably diminished due to events such as the Vietnam War. During that warm the Tet Offensive made U.S. citizens realize that North Vietnam was a strong nation with a powerful army, and they began to question the United States participation in the war. So yes, the significant event that pushed President Johnson to refuse reelection in the 1968 election was the New Hampshire Primary.