Note that the possible sums of two numbers, each 0 to 3, are 0 to 6 and analyse the possible ways to get each number:

To get 0, both numbers would have to be 0: probability (1/8)(1/8)= 1/64.

To get 1, one number would have to be 0 and the other 1: The probability that the first is 0 and the second 1 is (1/8)(1/4)= 1/32 but so is the other order. The probability one number is 0 and the other 1 is 2(1/32)= 1/16.

To get 2, one number could be 0 and the other 2 or both could be 1. There are three ways to do that: (0, 2), (1, 1), and (2, 0). The probabilites of each are (1/8)(1/8)= 1/64, (1/4)(1/4)= 1/16, and (1/8)(1/8)= 1/64. The probability of a 2 is 1/64+1/16+ 1/64= 3/32.

To get 3, one number must be 3 and the other 0 or one number 2 and the other 1. There are four ways to do that: (0, 3), (3, 0), (2, 1), and (1, 2). Calculate the probabilities of each of those and add.

Continue for 4, 5, and 6. As a check make sure the sum of all six probabilities is 1.