Alright, let's solve this problem step by step. We have 6366 and 1496 and we're adding them together.

Step 1: We'll start by adding the digits 6 & 6 in column 1 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 6 & 9 in column 2 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 3 & 4 in column 3 and get 8.

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

So, 6366 + 1496 = 7862.

