1. **State the problem:** Solve for the two possible values of $x$ in the equation $$(x - 3)(x - 8) = 0.$$\n\n2. **Formula and rule:** The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. That is, if $$A \times B = 0,$$ then either $$A = 0$$ or $$B = 0.$$\n\n3. **Apply the zero product property:** Set each factor equal to zero:\n$$x - 3 = 0$$\n$$x - 8 = 0$$\n\n4. **Solve each equation:**\nFor $$x - 3 = 0$$, add 3 to both sides:\n$$x = 3$$\n\nFor $$x - 8 = 0$$, add 8 to both sides:\n$$x = 8$$\n\n5. **Final answer:** The two possible values of $x$ are $$\boxed{3 \text{ and } 8}.$$