Okay, we are tasked with adding 9974 and 7451. 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 7 & 5 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 9 & 4 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 9 & 7 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 9974 + 7451 = 17425.

