Okay, we are tasked with adding 7754 and 4911. Let's begin!

Step 1: We'll start by adding the digits 4 & 1 in column 1 and get 5.

Step 2: We'll start by adding the digits 5 & 1 in column 2 and get 6.

Step 3: We'll start by adding the digits 7 & 9 in column 3 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 4 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 7754 + 4911 = 12665.

