Alright, let's solve this problem step by step. We have 1065 and 6676 and we're adding them together.

Step 1: We'll start by adding the digits 5 & 6 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 6 & 7 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 0 & 6 in column 3 and get 7.

Step 4: We'll start by adding the digits 1 & 6 in column 4 and get 7.

So, 1065 + 6676 = 7741.

