Okay, let's tackle this math problem. We're starting with 69643 and subtracting 35877.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 3 in column 1 and get -4.
We add -4 to 10 and get 6 as the first digit of the result.

Step 2: We'll start by subtracting the digit 7 and the borrow 1 from 4 in column 2 and get -4.
We add -4 to 10 and get 6 as the next digit of the result.

Step 3: We'll start by subtracting the digit 8 and the borrow 1 from 6 in column 3 and get -3.
We add -3 to 10 and get 7 as the next digit of the result.

Step 4: We'll start by subtracting the digit 5 and the borrow 1 from 9 in column 4 and get 3.
3 is the next digit of our result.

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

So, 69643 - 35877 = 33766.