Answer
52,457,600 number of plates.
Work Step by Step
Number of ways in which 2 English letters can be arranged = 26$\times$26
Number of ways in which 4 digits can be arranged = 10$\times$10$\times$10$\times$10
Plates with 2 letters followed by 4 digits = 26$\times$26$\times$10$\times$10$\times$10$\times$10=6760000
Number of ways in which 2 digits can be arranged = 10$\times$10
Number of ways in which 4 English letters can be arranged= 26$\times$26$\times$26$\times$26
Plates with 2 digits followed by 4 letters = 10$\times$10$\times$26$\times$26$\times$26$\times$26 = 45697600
Total number of plates = 6,760,000+45,697,600 = 52,457,600
