We have numbers 1604 and 8037. Let's start adding them together.

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

Step 2: We'll start by adding the digits 0 & 3 in column 2 and get 4.

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

Step 4: We'll start by adding the digits 1 & 8 in column 4 and get 9.

So, 1604 + 8037 = 9641.

