We are presented with 3440 and 677. Let's work out the sum.

Step 1: We'll start by adding the digits 0 & 7 in column 1 and get 7.

Step 2: We'll start by adding the digits 4 & 7 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 4 & 6 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

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

So, 3440 + 677 = 4117.

