Alright, let's solve this problem step by step. We have 2974 and 6496 and we're adding them together.

Step 1: We'll start by adding the digits 4 & 6 in column 1 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 9 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 9 & 4 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 2 & 6 in column 4 and get 9.

So, 2974 + 6496 = 9470.

