Okay, we are tasked with adding 1889 and 8680. Let's begin!

Step 1: We'll start by adding the digits 9 & 0 in column 1 and get 9.

Step 2: We'll start by adding the digits 8 & 8 in column 2 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 8 & 6 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 1 & 8 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 1889 + 8680 = 10569.

