We can solve this together! We're beginning with 69308 and removing 55891 from it.

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

Step 2: We'll start by subtracting the digit 9 and the borrow 0 from 0 in column 2 and get -9.
We add -9 to 10 and get 1 as the next digit of the result.

Step 3: We'll start by subtracting the digit 8 and the borrow 1 from 3 in column 3 and get -6.
We add -6 to 10 and get 4 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 5 and the borrow 0 from 6 in column 5 and get 1.
1 is the next digit of our result.

So, 69308 - 55891 = 13417.