How many license plates can be made using either two or three letters followed by either two or three digits?

20,077,200

Explanation:

We can resolve this problem multiplying:

We have 26 different letters in the alphabet, in the example says two letters and three letters, in addition, is followed by two or three digits, and there are 10 digits, the formula would be:

Using 2 letters and 2 digits is 26^2 X 10^2 = 67,600

Using 2 letters and 3 digits is 26^2 X 10^3 = 676,000

Using 3 letters and 2 digits is 26^3 X 10^2 = 1,757,600

Using 3 letters and 2 digits is 26^3 X 10^3 = 17,576,000

and the sum is 20,077,200