Let's break this down. We're going to add 6585 and 8434 together.

Step 1: We'll start by adding the digits 5 & 4 in column 1 and get 9.

Step 2: We'll start by adding the digits 8 & 3 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 4 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 6 & 8 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 6585 + 8434 = 15019.

