No problem, let's work through this together. We're starting with 636 and 7781 and adding them all up.

Step 1: We'll start by adding the digits 6 & 1 in column 1 and get 7.

Step 2: We'll start by adding the digits 3 & 8 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 6 & 7 in column 3 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 0 & 7 in column 4 and get 8.

So, 636 + 7781 = 8417.

