Alright, let's solve this problem step by step. We have 778 and 6163 and we're adding them together.

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

Step 2: We'll start by adding the digits 7 & 6 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 7 & 1 in column 3 and get 9.

Step 4: We'll start by adding the digits 0 & 6 in column 4 and get 6.

So, 778 + 6163 = 6941.

