1. **State the problem:** Solve the equation $6x6 = 9x$ for $x$. 2. **Write the equation:** $$6 \times 6 = 9x$$ 3. **Calculate the left side:** $$36 = 9x$$ 4. **Isolate $x$ by dividing both sides by 9:** $$\frac{36}{\cancel{9}} = \frac{9x}{\cancel{9}}$$ 5. **Simplify the division:** $$4 = x$$ 6. **Final answer:** $$x = 4$$ This means the value of $x$ that satisfies the equation is 4.