How many 6 character passwords using one letter a - h, and using 5 digits from digits 1- 9. I tried.?

The main question is whether you can repeat a digit.

If you can't repeat a digit, then yes, you would just multiply by 6! (the ways to arrange your 6 chosen items because they are all different).

Answer:
C(8,1) * C(9,5) * 6!

If you *can* repeat digits, then:

8 ways to pick a letter
6 choices of where that letter goes
9 choices for the digit to place in the first unused position
9 choices for the digit to place in the second unused position
9 choices for the digit to place in the third unused position
9 choices for the digit to place in the fourth unused position
9 choices for the digit to place in the fifth  unused position

Answer:
8 * 6 * 9^5

Choose the letter  ... 8 to pick from
5 digits  ... can they repeat?  if repeating is allowed  ... 9^5
  that gives  8 X 9^5 

if repeating is not allowed
   9X8X7X6X5  ways to pick the digits
  answer  ===  8X9X8X7X6X5   <<<  digits cannot repeat
   8 X 9^5  <<<  digits can repeat  <<<  I think is correct because nothing is mentined in the problem about repeating a digit..