Okay, we are tasked with adding 8034 and 7677. Let's begin!

Step 1: We'll start by adding the digits 4 & 7 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 3 & 7 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 6 in column 3 and get 7.

Step 4: We'll start by adding the digits 8 & 7 in column 4 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 8034 + 7677 = 15711.

