1. **State the problem:** Simplify the expression $$\frac{18h^2}{9h}$$. 2. **Recall the rule:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{18}{9} = \cancel{\frac{18}{9}}{2}$$. 4. **Simplify the variables:** $$\frac{h^2}{h} = h^{2-1} = h^1 = h$$. 5. **Combine the results:** $$2 \times h = 2h$$. **Final answer:** $$2h$$.