Alright, let's solve this problem step by step. We have 7497 and 4778 and we're adding them together.

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

Step 2: We'll start by adding the digits 9 & 7 in column 2 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 4 & 7 in column 3 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 4 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 7497 + 4778 = 12275.

