Okay, we are tasked with adding 8552 and 8624. Let's begin!

Step 1: We'll start by adding the digits 2 & 4 in column 1 and get 6.

Step 2: We'll start by adding the digits 5 & 2 in column 2 and get 7.

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 & 8 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 8552 + 8624 = 17176.

