Question

principle is used to find the number of strings of eight uppercase English letters that start or end with the letters BO (in that order), if letters can be repeated.

Answer 1

There are 6 other positions in the string, each with 26 choices. So if you fix BO as the first two letters, there are $26^6$ possible strings that you can make.

If BO is at the end of the string, you still have $26^6$ possible strings.

Together, then, you have $2\times26^6$ possible strings.