Which of the following is a run-on sentence?
In 1783, the US Congress ratified a preliminary peace treaty, the US and Britain signed the Treaty of Paris, British troops left New York City, and George Washington resigned as commander.
On April 19, 1783, the US Congress ratified a preliminary peace treaty, and the Treaty of Paris followed about five months later.
On September 3, 1783, The US and Britain signed the Treaty of Paris, and two months later, British troops left New York City.
On April 19, 1783, the US Congress ratified a preliminary peace treaty and five months later, the US and Britain signed the Treaty of Paris and British troops left New York City in November.

The answer to your question would be that the option that stands for example of a run-on sentence would be the following one: On April 19, 1783, the US Congress ratified a preliminary peace treaty and five months later, the US and Britain signed the Treaty of Paris and British troops left New York City in November.

This is a case of a comma splice. A comma splice occurs when two or more independent clauses are joined wtih just a comma. Take the example,

1) The US Congress ratified a preliminary peace treaty and five months later,

2) The US and Britain signed the Treaty of Paris and British troops left New York City in November.