Okay, we are tasked with adding 4508 and 7180. Let's begin!

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

Step 2: We'll start by adding the digits 0 & 8 in column 2 and get 8.

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

Step 4: We'll start by adding the digits 4 & 7 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 4508 + 7180 = 11688.

