Okay, we are tasked with adding 3538 and 8537. Let's begin!

Step 1: We'll start by adding the digits 8 & 7 in column 1 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 3 & 3 in column 2 and get 7.

Step 3: We'll start by adding the digits 5 & 5 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 3 & 8 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 3538 + 8537 = 12075.

