Let's break this down. We're going to add 9590 and 4334 together.

Step 1: We'll start by adding the digits 0 & 4 in column 1 and get 4.

Step 2: We'll start by adding the digits 9 & 3 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 3 in column 3 and get 9.

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

So, 9590 + 4334 = 13924.

