Okay, we are tasked with adding 8631 and 8088. Let's begin!

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

Step 2: We'll start by adding the digits 3 & 8 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 6 & 0 in column 3 and get 7.

Step 4: We'll start by adding the digits 8 & 8 in column 4 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

So, 8631 + 8088 = 16719.

