1. **State the problem:** Solve the equation $ (z - 4)(z - 6) = 0 $. 2. **Formula and rule:** The zero product property states that if $ab = 0$, then either $a = 0$ or $b = 0$. 3. **Apply the zero product property:** Set each factor equal to zero: $$ z - 4 = 0 $$ $$ z - 6 = 0 $$ 4. **Solve each equation:** $$ z = 4 $$ $$ z = 6 $$ 5. **Final answer:** The solutions to the equation are $z = 4$ and $z = 6$.