Okay, we are tasked with adding 4290 and 8539. Let's begin!

Step 1: We'll start by adding the digits 0 & 9 in column 1 and get 9.

Step 2: We'll start by adding the digits 9 & 3 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 2 & 5 in column 3 and get 8.

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

So, 4290 + 8539 = 12829.

