Okay, we are tasked with adding 1982 and 8475. Let's begin!

Step 1: We'll start by adding the digits 2 & 5 in column 1 and get 7.

Step 2: We'll start by adding the digits 8 & 7 in column 2 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 9 & 4 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 1 & 8 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 1982 + 8475 = 10457.

