We have numbers 5909 and 9266. Let's start adding them together.

Step 1: We'll start by adding the digits 9 & 6 in column 1 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 0 & 6 in column 2 and get 7.

Step 3: We'll start by adding the digits 9 & 2 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 5 & 9 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 5909 + 9266 = 15175.

