Article snapshot taken from Wikipedia with creative commons attribution-sharealike license.
Give it a read and then ask your questions in the chat.
We can research this topic together.
Texas voted for the Liberal Republican nominee Horace Greeley, who received 57% of the vote. However, Greeley died before the electors could cast their votes for president and vice president. Since it was already clear long before Greeley's death that incumbent Republican President Ulysses S. Grant had easily won re-election in any case, Texan electors (along with the electors of five other states) were effectively left free to vote for whoever they chose. All eight electors voted for Thomas A. Hendricks.
This was the first presidential election since 1860 that Texas participated in. It had seceded from the United States in March 1861 and joined the Confederate States of America during the American Civil War. It would not participate in the following elections in 1864 and 1868 and would not be readmitted into the Union until 1870.
This was the first presidential election in Texas in which the Republican nominee was on the ballot. President Grant finished a respectable second with over 40% of the vote, which ultimately stood as the best performance for a Republican candidate for over half a century until Republican Herbert Hoover won the state in 1928 as part of anti-Catholic surge against Democratic nominee Al Smith.
This remains the most recent election in which Texas's electoral votes went to a Democrat while neighboring Arkansas voted Republican.
^ Greeley died after the election, but prior to the Electoral College meeting, and was thus ineligible for the office of President. Greeley had won 8 pledged electors, of which all cast their votes for other Democrats.