Okay, we are tasked with adding 369 and 8473. Let's begin!

Step 1: We'll start by adding the digits 9 & 3 in column 1 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 6 & 7 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 3 & 4 in column 3 and get 8.

Step 4: We'll start by adding the digits 0 & 8 in column 4 and get 8.

So, 369 + 8473 = 8842.

