1. The problem is to solve the expression labeled as number 8: $$8m^2 - 6m - 9$$ and verify if it equals the product $$(2m - 3)(4m + 3)$$. 2. First, recall the distributive property (FOIL method) for multiplying binomials: $$(a + b)(c + d) = ac + ad + bc + bd$$. 3. Apply this to $$(2m - 3)(4m + 3)$$: $$= 2m \times 4m + 2m \times 3 - 3 \times 4m - 3 \times 3$$ $$= 8m^2 + 6m - 12m - 9$$ 4. Combine like terms: $$8m^2 + (6m - 12m) - 9 = 8m^2 - 6m - 9$$ 5. This matches the original expression exactly, so: $$8m^2 - 6m - 9 = (2m - 3)(4m + 3)$$ 6. Therefore, the factorization is correct and the expression is solved by factoring as shown.