Okay, we are tasked with adding 8197 and 4441. Let's begin!

Step 1: We'll start by adding the digits 7 & 1 in column 1 and get 8.

Step 2: We'll start by adding the digits 9 & 4 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 4 in column 3 and get 6.

Step 4: We'll start by adding the digits 8 & 4 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 8197 + 4441 = 12638.

