What problems did the elections of 1796 and 1800 highlight about our first system for electing the President and Vice President? How did the 12th amendment solve these problems?

The correct answer to this open question is the following.

Although there are no options attached, we can say the following.

The problems that the elections of 1796 and 1800 highlighted about our first system for electing the President and Vice President were bitter rivalries, attempts to manipulate the Electoral College and the elections, and political differences and conflicts.

In 1796, the US President George Washington decide not to participate in the next election, which opened the doors to John Jay and Thomas Jefferson to compete in the election and was the beginning of parties and factions that Washington critique and did not want that to happen in the United States.

The 12th amendment to the United States Constitution solved these problems because it established separate votes for President and vice president in the Electoral College, not the popular vote, in order to eliminate the many problems of the elections of 1796 and 1800. The amendment was ratified on June 15, 1804.