Okay, we are tasked with adding 9180 and 6874. Let's begin!

Step 1: We'll start by adding the digits 0 & 4 in column 1 and get 4.

Step 2: We'll start by adding the digits 8 & 7 in column 2 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 8 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 9 & 6 in column 4 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

So, 9180 + 6874 = 16054.

