We can solve this together! We're beginning with 6677 and removing 4107 from it.

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

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

Step 3: We'll start by subtracting the digit 1 and the borrow 0 from 6 in column 3 and get 5.
5 is the next digit of our result.

Step 4: We'll start by subtracting the digit 4 and the borrow 0 from 6 in column 4 and get 2.
2 is the next digit of our result.

So, 6677 - 4107 = 2570.