We are presented with 4944 and 819. Let's work out the sum.

Step 1: We'll start by adding the digits 4 & 9 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 4 & 1 in column 2 and get 6.

Step 3: We'll start by adding the digits 9 & 8 in column 3 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 4 & 0 in column 4 and get 5.

So, 4944 + 819 = 5763.

