No problem, let's work through this together. We're starting with 7410 and 8177 and adding them all up.

Step 1: We'll start by adding the digits 0 & 7 in column 1 and get 7.

Step 2: We'll start by adding the digits 1 & 7 in column 2 and get 8.

Step 3: We'll start by adding the digits 4 & 1 in column 3 and get 5.

Step 4: We'll start by adding the digits 7 & 8 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 7410 + 8177 = 15587.

