Okay, we are tasked with adding 7686 and 8917. Let's begin!

Step 1: We'll start by adding the digits 6 & 7 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

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

Step 3: We'll start by adding the digits 6 & 9 in column 3 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 8 in column 4 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

So, 7686 + 8917 = 16603.

