Alright, let's solve this problem step by step. We have 7966 and 6945 and we're adding them together.

Step 1: We'll start by adding the digits 6 & 5 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 & 4 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 9 & 9 in column 3 and get 19.
We'll write down the last digit 9 and carry the 1 to the next column.

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

So, 7966 + 6945 = 14911.

