Alright, let's solve this problem step by step. We have 6303 and 1543 and we're adding them together.

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

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

Step 3: We'll start by adding the digits 3 & 5 in column 3 and get 8.

Step 4: We'll start by adding the digits 6 & 1 in column 4 and get 7.

So, 6303 + 1543 = 7846.

