Okay, we are tasked with adding 5178 and 4492. Let's begin!

Step 1: We'll start by adding the digits 8 & 2 in column 1 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 9 in column 2 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 4 in column 3 and get 6.

Step 4: We'll start by adding the digits 5 & 4 in column 4 and get 9.

So, 5178 + 4492 = 9670.

