Okay, we are tasked with adding 8919 and 2825. Let's begin!

Step 1: We'll start by adding the digits 9 & 5 in column 1 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 2 in column 2 and get 4.

Step 3: We'll start by adding the digits 9 & 8 in column 3 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 8 & 2 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 8919 + 2825 = 11744.

