Okay, let's tackle this math problem. We're starting with 8977 and subtracting 7775.

Step 1: We'll start by subtracting the digit 5 and the borrow 0 from 7 in column 1 and get 2.
2 is the first digit of our result.

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

Step 3: We'll start by subtracting the digit 7 and the borrow 0 from 9 in column 3 and get 2.
2 is the next digit of our result.

Step 4: We'll start by subtracting the digit 7 and the borrow 0 from 8 in column 4 and get 1.
1 is the next digit of our result.

So, 8977 - 7775 = 1202.