We are presented with 665 and 7769. Let's work out the sum.

Step 1: We'll start by adding the digits 5 & 9 in column 1 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 6 & 6 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 6 & 7 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 0 & 7 in column 4 and get 8.

So, 665 + 7769 = 8434.

