During the War of 1812, the American flag had 15 stars.
The 15-star, 15-stripe design became official in 1795 after Vermont and Kentucky joined the United States. It remained the national flag throughout the War of 1812, even though the modern flag has 50 stars and only 13 stripes.
The famous Star-Spangled Banner flown over Fort McHenry during the Battle of Baltimore in September 1814 was a huge example of this design. Its 15 stars and 15 stripes inspired Francis Scott Key to write the poem that became the national anthem.
Congress later returned the flag to 13 stripes in 1818, while continuing to add one star for each new state. That is why 15, rather than 13 or 18, is the standard answer for the War of 1812 era.