Okay, we are tasked with adding 2177 and 6579. Let's begin!

Step 1: We'll start by adding the digits 7 & 9 in column 1 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 7 in column 2 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 5 in column 3 and get 7.

Step 4: We'll start by adding the digits 2 & 6 in column 4 and get 8.

So, 2177 + 6579 = 8756.

