It is given that a computer password must be eight characters long. We are supposed to use only the 26 letters of the alphabet. No where has it been mentioned that repetition of letters is not allowed. Thus, assuming repetition of letters, we can see that the any of the eight letters of the password can be any one of the 26 letters of the alphabet.
Therefore, the first letter of the password can be put in 26 ways.
Likewise, the second letter of the password too can be put in 26 ways, so on and so forth.
Therefore, the total possibilities of an 8 letter password will become:
Which is approximately, 208 Billion!