Let's break this down. We're going to add 2577 and 8271 together.

Step 1: We'll start by adding the digits 7 & 1 in column 1 and get 8.

Step 2: We'll start by adding the digits 7 & 7 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 2 in column 3 and get 8.

Step 4: We'll start by adding the digits 2 & 8 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 2577 + 8271 = 10848.

