We have numbers 6974 and 3006. Let's start adding them together.

Step 1: We'll start by adding the digits 4 & 6 in column 1 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 0 in column 2 and get 8.

Step 3: We'll start by adding the digits 9 & 0 in column 3 and get 9.

Step 4: We'll start by adding the digits 6 & 3 in column 4 and get 9.

So, 6974 + 3006 = 9980.

