1. **State the problem:** Simplify the expression $$\frac{4a^4 + 8a^4}{6a^2}$$. 2. **Combine like terms in the numerator:** Since both terms have $a^4$, add the coefficients: $$4a^4 + 8a^4 = (4 + 8)a^4 = 12a^4$$ 3. **Rewrite the expression:** $$\frac{12a^4}{6a^2}$$ 4. **Simplify the fraction by dividing numerator and denominator coefficients:** $$\frac{\cancel{12}a^4}{\cancel{6}a^2} = \frac{2a^4}{a^2}$$ 5. **Simplify the powers of $a$ using the rule $\frac{a^m}{a^n} = a^{m-n}$:** $$2a^{4-2} = 2a^2$$ 6. **Final answer:** $$2a^2$$ This means the original expression simplifies to $2a^2$.