We have numbers 3004 and 1959. Let's start adding them together.

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 0 & 5 in column 2 and get 6.

Step 3: We'll start by adding the digits 0 & 9 in column 3 and get 9.

Step 4: We'll start by adding the digits 3 & 1 in column 4 and get 4.

So, 3004 + 1959 = 4963.

