1. **State the problem:** Penelope rolls four regular six-sided dice (each numbered 1 to 6) and sums the dots on the top faces. We want to find how many different possible sums she can get. 2. **Understand the range of sums:** Each die can show a minimum of 1 and a maximum of 6. - Minimum sum: $4 \times 1 = 4$ - Maximum sum: $4 \times 6 = 24$ 3. **Possible sums:** Since each die is independent and the sum is the total of four dice, the sums can range from 4 to 24. 4. **Are all sums between 4 and 24 possible?** Yes, because by adjusting the dice values, every integer sum between 4 and 24 can be formed. 5. **Count the number of possible sums:** The sums are all integers from 4 up to 24 inclusive. Number of possible sums = $24 - 4 + 1 = 21$ **Final answer:** Penelope can obtain **21** different possible sums when rolling four six-sided dice.