Okay, we are tasked with adding 7857 and 1666. 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 5 & 6 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 8 & 6 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 1 in column 4 and get 9.

So, 7857 + 1666 = 9523.

