Okay, we are tasked with adding 8054 and 9081. 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 0 & 0 in column 3 and get 1.

Step 4: We'll start by adding the digits 8 & 9 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 8054 + 9081 = 17135.

