Okay, we are tasked with adding 429 and 6990. Let's begin!

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

Step 2: We'll start by adding the digits 2 & 9 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 4 & 9 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 0 & 6 in column 4 and get 7.

So, 429 + 6990 = 7419.

