Final answer:
The War with Mexico began with a clash between U.S. and Mexican forces at the Rio Grande, resulting in the death or injury of sixteen U.S. soldiers.
Step-by-step explanation:
The incident that began the war with Mexico was the clash between the U.S. force ordered to the banks of the Rio Grande and a Mexican cavalry unit in January 1846.
This clash resulted in the death or injury of sixteen U.S. soldiers. President Polk used this incident as a justification to declare war on Mexico, stating that Mexico had invaded U.S. territory and shed American blood upon American soil.
On May 12, 1846, Congress approved the declaration of war on Mexico.