Okay, we are tasked with adding 2814 and 9538. Let's begin!

Step 1: We'll start by adding the digits 4 & 8 in column 1 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 3 in column 2 and get 5.

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

Step 4: We'll start by adding the digits 2 & 9 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 2814 + 9538 = 12352.

