I concur with Pohnpei, the best answer in this case is B. The president was shocked by U.S. losses in the Tet Offensive. The war in Vietnam brought about a myriad of challenges to the president. These challenges caused the rapid drop in popularity for the presidency among the citizens. During his campaigns, the president had assured the public that he would not expand the United States involvement in Vietnam. He however, did not adhere to his plan, and this resulted in massive losses for the U.S. in Vietnam. The country suffered increasing casualties and negative financial effects caused by the expansion efforts in Vietnam.
The defeat during the Tet offensive offered more opportunities to his opponents to continue challenging the United States involvement in Vietnam. The general population was sharply divided on the issue, with some of the most influential politicians, such as Robert F. Kennedy, increasingly campaigning against the war in Vietnam.
The best of the answers that you give us is B. Johnson definitely withdrew from the 1968 presidential election because of the fact that the country was coming to dislike his policies in Vietnam more and more. This led him to believe that he had to withdraw from the race as a way of atoning for the fact that his policies were not working. As the link below says,
The war in Vietnam had taken a heavy toll on him. It had cost him his credibility, and it had eroded his political authority to the point where he could no longer govern effectively. All that remained to be salvaged was what mattered most to him—the respect of his 'fellow Americans.'
Part of what lost him his credibility was the Tet Offensive. Johnson and his government had been assuring the American people that their strategy was working and that the war was almost over. When the Tet Offensive showed that this was not really true, Johnson lost much of his credibility with the American people.