Okay, we are given 4190 and 5580. Let's add them up step by step.

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

Step 2: We'll start by adding the digits 9 & 8 in column 2 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 5 in column 3 and get 7.

Step 4: We'll start by adding the digits 4 & 5 in column 4 and get 9.

So, 4190 + 5580 = 9770.

