Okay, let's tackle this math problem. We're starting with 10744 and subtracting 6639.

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

Step 2: We'll start by subtracting the digit 3 and the borrow 1 from 4 in column 2 and get 0.
0 is the next digit of our result.

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

Step 4: We'll start by subtracting the digit 6 and the borrow 0 from 0 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 0 and the borrow 1 from 1 in column 5 and get 0.
0 is the next digit of our result.

So, 10744 - 6639 = 4105.