Okay, we are tasked with adding 4082 and 4999. Let's begin!

Step 1: We'll start by adding the digits 2 & 9 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 8 & 9 in column 2 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

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

Step 4: We'll start by adding the digits 4 & 4 in column 4 and get 9.

So, 4082 + 4999 = 9081.

