1. Add and Simplify the polynomials: $ (3h^2 - 6h) + (5h + 9h^2 - 7) $ 2. Combine like terms by grouping powers of $h$: $$3h^2 + 9h^2 - 6h + 5h - 7$$ 3. Simplify each group: $$ (3h^2 + 9h^2) + (-6h + 5h) - 7 = 12h^2 - h - 7$$ Final answer: $$12h^2 - h - 7$$