Okay, we are tasked with adding 8582 and 9613. Let's begin!

Step 1: We'll start by adding the digits 2 & 3 in column 1 and get 5.

Step 2: We'll start by adding the digits 8 & 1 in column 2 and get 9.

Step 3: We'll start by adding the digits 5 & 6 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 8 & 9 in column 4 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

So, 8582 + 9613 = 18195.

