No problem, let's work through this together. We're starting with 3643 and 6586 and adding them all up.

Step 1: We'll start by adding the digits 3 & 6 in column 1 and get 9.

Step 2: We'll start by adding the digits 4 & 8 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 6 & 5 in column 3 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 3 & 6 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 3643 + 6586 = 10229.

