Okay, we are tasked with adding 7808 and 3044. Let's begin!

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

Step 2: We'll start by adding the digits 0 & 4 in column 2 and get 5.

Step 3: We'll start by adding the digits 8 & 0 in column 3 and get 8.

Step 4: We'll start by adding the digits 7 & 3 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 7808 + 3044 = 10852.

