1. **State the problem:** Simplify the expression $$12 - \frac{8y^{7}z^{2}}{24y^{2}}$$. 2. **Identify the formula and rules:** When simplifying expressions with fractions, divide numerator and denominator by their greatest common factors and apply the laws of exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$. 3. **Simplify the fraction:** $$\frac{8y^{7}z^{2}}{24y^{2}} = \frac{\cancel{8} \cdot y^{7} \cdot z^{2}}{\cancel{24} \cdot y^{2}} = \frac{1 \cdot y^{7} \cdot z^{2}}{3 \cdot y^{2}}$$ 4. **Apply exponent subtraction:** $$= \frac{y^{7}}{y^{2}} \cdot \frac{z^{2}}{3} = y^{7-2} \cdot \frac{z^{2}}{3} = y^{5} \cdot \frac{z^{2}}{3} = \frac{y^{5}z^{2}}{3}$$ 5. **Rewrite the original expression:** $$12 - \frac{y^{5}z^{2}}{3}$$ 6. **Express 12 as a fraction with denominator 3:** $$12 = \frac{36}{3}$$ 7. **Combine the terms:** $$\frac{36}{3} - \frac{y^{5}z^{2}}{3} = \frac{36 - y^{5}z^{2}}{3}$$ **Final simplified expression:** $$\boxed{\frac{36 - y^{5}z^{2}}{3}}$$