Put these events in their proper order (1-9). alamo falls to santa anna harrison elected president settlement of texas tyler becomes president annexation of texas accident aboard the uss princeton polk elected president santa anna defeated at san jacinto tyler leaves democratic party

Let's look at a brief summary of each of the events you were given.

Alamo falls to Santa Anna
During the Battle of the Alamo, Mexican troops attacked the Alamo Mission and killed all of the defenders there. The Alamo fell to Mexican President General Antonio Lopez de Santa Anna on March 6, 1836.

Harrison elected President
After resigning from the army, William Henry Harrison was elected to the U.S. House of Representatives. From there he became a state senator, then moved to U.S. minister to Colombia. Harrison then ran for president and was elected in 1840. 

Settlement of Texas
Although Native Americans and Mexicans lived on land in Texas previously, the American settlement came later. At the age of 24, Stephen Austin brought 300 families to settle in Texas in 1817. 

Tyler becomes President 
Vice President John Tyler took over the Presidency after William Henry Harrison passed away from pneumonia. Tyler was inaugurated April 6, 1841. 

Annexation of Texas
Texas was admitted to the United States as the 28th state on December 29, 1845. 

Accident aboard the USS Princeton
The USS Princeton was a Navy warship. On February 28, 1844, during a showing of the guns, one of them exploded and killed 6 people. 

Polk elected President 
Democrat James K. Polk defeated Henry Clay in the presidential election of December of 1844. 

Santa Anna defeated at San Jacinto
The Texian Army met and defeated the Mexican army at the Battle of San Jacinto. The battle on April 21, 1836 only lasted 18 minutes.

Tyler leaves Democratic Party
John Tyler began as a Democrat but disagreed with Andrew Jackson's choices during the Nullification Crisis when South Carolina threatened secession. For this he left the Democratic Party to become part of the Whig Party in 1834. 

Now, we just need to put these events in order:
1. 1817 Settlement of Texas
2. 1834 John Tyler leaves Democratic Party
3. March 6, 1836 Alamo falls to Santa Anna
4. April 21, 1836 Santa Anna defeated at San Jacinto
5. 1840 Harrison becomes President
6. April 6, 1841  Tyler becomes President
7. February 28, 1844 Accident aboard the USS Princeton
8. December 1844 Polk elected President
8. December 29, 1845 Annexation of Texas