Okay, let's tackle this math problem. We're starting with 7744 and subtracting 4762.

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

Step 2: We'll start by subtracting the digit 6 and the borrow 0 from 4 in column 2 and get -2.
We add -2 to 10 and get 8 as the next digit of the result.

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

Step 4: We'll start by subtracting the digit 4 and the borrow 1 from 7 in column 4 and get 2.
2 is the next digit of our result.

So, 7744 - 4762 = 2982.