Okay, let's tackle this math problem. We're starting with 191735 and subtracting 17099.

Step 1: We'll start by subtracting the digit 9 and the borrow 0 from 5 in column 1 and get -4.
We add -4 to 10 and get 6 as the first digit of the result.

Step 2: We'll start by subtracting the digit 9 and the borrow 1 from 3 in column 2 and get -7.
We add -7 to 10 and get 3 as the next digit of the result.

Step 3: We'll start by subtracting the digit 0 and the borrow 1 from 7 in column 3 and get 6.
6 is the next digit of our result.

Step 4: We'll start by subtracting the digit 7 and the borrow 0 from 1 in column 4 and get -6.
We add -6 to 10 and get 4 as the next digit of the result.

Step 5: We'll start by subtracting the digit 1 and the borrow 1 from 9 in column 5 and get 7.
7 is the next digit of our result.

Step 6: We'll start by subtracting the digit 0 and the borrow 0 from 1 in column 6 and get 1.
1 is the next digit of our result.

So, 191735 - 17099 = 174636.