1. **State the problem:** Olive flips a coin and rolls a number cube with numbers 1 to 6. We want to find the probability that she flips heads and rolls an even number. 2. **Understand the sample space:** The coin has 2 outcomes: Heads (H) or Tails (T). The number cube has 6 outcomes: 1, 2, 3, 4, 5, 6. Total possible outcomes = $2 \times 6 = 12$. 3. **Identify favorable outcomes:** We want outcomes where the coin shows Heads and the number is even. Even numbers on the cube are 2, 4, and 6. Favorable outcomes: H2, H4, H6. Number of favorable outcomes = 3. 4. **Calculate the probability:** Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{12}$. 5. **Simplify the fraction:** $$\frac{3}{12} = \frac{\cancel{3}}{\cancel{12}} = \frac{1}{4}$$ 6. **Final answer:** The probability that Olive flipped heads and rolled an even number is $\boxed{\frac{1}{4}}$.