Okay, we are tasked with adding 4218 and 4863. Let's begin!

Step 1: We'll start by adding the digits 8 & 3 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 1 & 6 in column 2 and get 8.

Step 3: We'll start by adding the digits 2 & 8 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, 4218 + 4863 = 9081.

