Okay, we are tasked with adding 4179 and 5518. Let's begin!

Step 1: We'll start by adding the digits 9 & 8 in column 1 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 1 in column 2 and get 9.

Step 3: We'll start by adding the digits 1 & 5 in column 3 and get 6.

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

So, 4179 + 5518 = 9697.

