Okay, we are tasked with adding 8544 and 8829. Let's begin!

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

Step 2: We'll start by adding the digits 4 & 2 in column 2 and get 7.

Step 3: We'll start by adding the digits 5 & 8 in column 3 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 8 & 8 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 8544 + 8829 = 17373.

