Okay, we are given 4519 and 4977. Let's add them up step by step.

Step 1: We'll start by adding the digits 9 & 7 in column 1 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 7 in column 2 and get 9.

Step 3: We'll start by adding the digits 5 & 9 in column 3 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

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

So, 4519 + 4977 = 9496.

