Okay, we are tasked with adding 4554 and 5081. Let's begin!

Step 1: We'll start by adding the digits 4 & 1 in column 1 and get 5.

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 & 0 in column 3 and get 6.

Step 4: We'll start by adding the digits 4 & 5 in column 4 and get 9.

So, 4554 + 5081 = 9635.

