Alright, let's solve this problem step by step. We have 7970 and 6419 and we're adding them together.

Step 1: We'll start by adding the digits 0 & 9 in column 1 and get 9.

Step 2: We'll start by adding the digits 7 & 1 in column 2 and get 8.

Step 3: We'll start by adding the digits 9 & 4 in column 3 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 6 in column 4 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

So, 7970 + 6419 = 14389.

