1. **State the problem:** Find the highest common factor (HCF) of $y^6$ and $y^9$. 2. **Recall the formula:** The HCF of two powers with the same base is the base raised to the minimum of the two exponents. 3. **Apply the rule:** Here, the base is $y$, and the exponents are 6 and 9. 4. **Calculate:** The minimum exponent is $\min(6,9) = 6$. 5. **Write the HCF:** Therefore, the HCF is $$y^6$$. **Final answer:** The highest common factor of $y^6$ and $y^9$ is $$y^6$$.