1. **State the problem:** Solve for $4x$ given the equation $2x + 15 = 7(4x - 9)$. 2. **Write the equation:** $$2x + 15 = 7(4x - 9)$$ 3. **Distribute the 7 on the right side:** $$2x + 15 = 7 \times 4x - 7 \times 9$$ $$2x + 15 = 28x - 63$$ 4. **Bring all terms involving $x$ to one side and constants to the other:** $$2x - 28x = -63 - 15$$ $$-26x = -78$$ 5. **Divide both sides by $-26$ to solve for $x$:** $$x = \frac{-78}{-26}$$ $$x = \cancel{\frac{-78}{-26}} \Rightarrow x = 3$$ 6. **Find $4x$ by multiplying $x$ by 4:** $$4x = 4 \times 3 = 12$$ **Final answer:** $$\boxed{12}$$