Answer
$6,760,000$ different license plates.
Work Step by Step
First character (a letter): 26 choices
Second character (a letter): 26 choices
Third character (a digit): 10 choices
Fourth character (a digit): 10 choices
Fifth character (a digit): 10 choices
Sixth character (a digit): 10 choices
Using the Multiplication Rule of Counting (see page 298):
$26\times26\times10\times10\times10\times10=6,760,000$
