How did the Fifteenth Amendment benefit Ulysses S. Grant in winning the presidency in 1868?

The Fifteenth Amendment, which gave African-American men the right to vote, did not benefit Ulysses S. Grant in the Presidential election of 1868, because it had not yet been passed by Congress. That actually happened in 1869, and the Amendment, having been ratified by the states, went into effect in 1870. Very few black men were allowed to vote anywhere in the United States (including Northern states) in 1868.

However, African-Americans could and did vote in the Presidential election of 1872, when their votes helped secure Grant's reelection by a very comfortable electoral margin, including most states in the South. In the years following this election, however, the fall of Reconstruction in the South would be followed by new methods of disfranchising African-American voters. These methods, which included terror and intimidation as well as literacy tests and poll taxes, were essential to the establishment of a Jim Crow white supremacist society in the South.