Okay, we are tasked with adding 8179 and 4490. 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 7 & 9 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 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, 8179 + 4490 = 12669.

