Okay, we are tasked with adding 4190 and 8578. Let's begin!

Step 1: We'll start by adding the digits 0 & 8 in column 1 and get 8.

Step 2: We'll start by adding the digits 9 & 7 in column 2 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 5 in column 3 and get 7.

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, 4190 + 8578 = 12768.

