Okay, we are tasked with adding 8670 and 8818. Let's begin!

Step 1: We'll start by adding the digits 0 & 8 in column 1 and get 8.

Step 2: We'll start by adding the digits 7 & 1 in column 2 and get 8.

Step 3: We'll start by adding the digits 6 & 8 in column 3 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 8 & 8 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 8670 + 8818 = 17488.

