Okay, let's tackle this math problem. We're starting with 637991 and subtracting 13408.

Step 1: We'll start by subtracting the digit 8 and the borrow 0 from 1 in column 1 and get -7.
We add -7 to 10 and get 3 as the first digit of the result.

Step 2: We'll start by subtracting the digit 0 and the borrow 1 from 9 in column 2 and get 8.
8 is the next digit of our result.

Step 3: We'll start by subtracting the digit 4 and the borrow 0 from 9 in column 3 and get 5.
5 is the next digit of our result.

Step 4: We'll start by subtracting the digit 3 and the borrow 0 from 7 in column 4 and get 4.
4 is the next digit of our result.

Step 5: We'll start by subtracting the digit 1 and the borrow 0 from 3 in column 5 and get 2.
2 is the next digit of our result.

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

So, 637991 - 13408 = 624583.