Make a probability distribution for the given set of events.

The probability of getting any one side is 1/4.

Sum of 4:

The only way to get a sum of 4, is if both dice land on 2. That's 1/4 in the first dice, and 1/4 in the other. Combining these probabilities using the fundamental counting principle, it's (1/4)*(1/4) = 1/16.

For a sum of six

To make 6, you need to get 2 in one dice and 4 in the other. That's the only way it could happen.

(1/4)*(1/4) = 1/16

For a sum of 8:

This can happen in two ways:

(1) if you role 2 with the first dice, 6 with dice two

(1/4)*(1/4) = 1/16

(2) if you role 4 and 4

(1/4)*(1/4) = 1/16

Now add these probabilities up: (1/16)+(1/16) = 1/8

For a sum of 10:

Possibilities:

2, 8 (1/16)

2, 4 (1/16)

2, 6 (1/16)

4, 6 (1/16)

Add those up, you get 4/16 or simply 1/4

Sum of 12:

Possibilities

4, 8 (1/16)

6, 6 (1/16)

Add them: 1/8 (simplified)

Sum of 14:

6, 8 (1/16)

Therefore, 1/16 chance of this

Sum of 16:

8, 8 ONLY

Therefore, 1/16 chance.

Let me know if this makes sense to you!