We can solve this together! We're beginning with 397877 and removing 35103 from it.

Step 1: We'll start by subtracting the digit 3 and the borrow 0 from 7 in column 1 and get 4.
4 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 8 in column 3 and get 7.
7 is the next digit of our result.

Step 4: We'll start by subtracting the digit 5 and the borrow 0 from 7 in column 4 and get 2.
2 is the next digit of our result.

Step 5: We'll start by subtracting the digit 3 and the borrow 0 from 9 in column 5 and get 6.
6 is the next digit of our result.

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

So, 397877 - 35103 = 362774.