Because the last digit is only the multiplication of the last two digits. So we can directly intercept the last digit of 2002, 2.

Square: 2×2=4

Cube: 4×2=8

Power 4: 8×2= 16

Quintic: 16×2=32

6th power: 32×2=64

…

We find that in the subsequent calculation, the last digit is cyclic, and the cyclic digits are 2.4.8.6 in turn, so we can get that the power of 2002 and 2006 is 2006 divided by 4=50 1+2, and its last digit is the second digit of 2.4.8.6, which is 4.

Similarly, we can draw that the last place of the 2008 power of 2002 is the fourth place of 2.4.8.6, which is 6.

Original handmade, hope to adopt. Thank you.