Okay, we are tasked with adding 4556 and 3882. Let's begin!

Step 1: We'll start by adding the digits 6 & 2 in column 1 and get 8.

Step 2: We'll start by adding the digits 5 & 8 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 8 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 4 & 3 in column 4 and get 8.

So, 4556 + 3882 = 8438.

