Okay, we are tasked with adding 477 and 1586. Let's begin!

Step 1: We'll start by adding the digits 7 & 6 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 7 & 8 in column 2 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 4 & 5 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 0 & 1 in column 4 and get 2.

So, 477 + 1586 = 2063.

