Alright, let's solve this problem step by step. We have 6826 and 6001 and we're adding them together.

Step 1: We'll start by adding the digits 6 & 1 in column 1 and get 7.

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

Step 3: We'll start by adding the digits 8 & 0 in column 3 and get 8.

Step 4: We'll start by adding the digits 6 & 6 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 6826 + 6001 = 12827.

