We can solve this together! We're beginning with 77807 and removing 66381 from it.

Step 1: We'll start by subtracting the digit 1 and the borrow 0 from 7 in column 1 and get 6.
6 is the first digit of our result.

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

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

Step 4: We'll start by subtracting the digit 6 and the borrow 0 from 7 in column 4 and get 1.
1 is the next digit of our result.

Step 5: We'll start by subtracting the digit 6 and the borrow 0 from 7 in column 5 and get 1.
1 is the next digit of our result.

So, 77807 - 66381 = 11426.