Okay, let's tackle this math problem. We're starting with 71176 and subtracting 4913.

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

Step 2: We'll start by subtracting the digit 1 and the borrow 0 from 7 in column 2 and get 6.
6 is the next digit of our result.

Step 3: We'll start by subtracting the digit 9 and the borrow 0 from 1 in column 3 and get -8.
We add -8 to 10 and get 2 as the next digit of the result.

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

Step 5: We'll start by subtracting the digit 0 and the borrow 1 from 7 in column 5 and get 6.
6 is the next digit of our result.

So, 71176 - 4913 = 66263.