SOLUTION: how many 2 digit numbers and single digit numbers can you get out of a 7 digit number, in a set of 6 numbers consisting of both single and double digit numbers with the highest num

Something is missing.

If the 7 digit number is 1234569 the answer will be different than if the
7-digit number is 1456789.

Since each set contains 6 numbers, and there are only 7 digits available, we
can only have 5 single digit numbers and only one double-digit number.

Every set of 6 is of this form (A,B,C,D,E,FG}, 5 single digits and 1 double-
digit number FG.

The most restrictive digit is our choice for F.  So we choose it first.

If the 7-digit number were 1234569 we could choose F any of 5 ways, since the
2-digit number must not exceed 59.  However if the 7-digit number were 1456789
we could choose F only 2 ways. 

So if the 7-digit number were 1234569 the answer would be 5×6! but if the 
7-digit number were 1456789, the answer would be 2×6!.

Can you explain it better in the thank-you note, stating it exactly 
word-for-word, number-for-number the way your teacher gave it to you? If so,
I'll be glad to help you, but as it is stated here, there is no way.

Edwin