1. **State the problem:** Simplify the expression $$[(4a^4)(2a^3)]^2$$. 2. **Use the product rule for exponents:** When multiplying terms with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. **Multiply the constants and variables inside the parentheses:** $$ (4a^4)(2a^3) = 4 \times 2 \times a^{4+3} = 8a^7 $$ 4. **Now raise the result to the power of 2:** $$ (8a^7)^2 = 8^2 \times (a^7)^2 $$ 5. **Use the power rule for exponents:** When raising a power to another power, multiply the exponents: $$ (a^m)^n = a^{m \times n} $$ 6. **Calculate each part:** $$ 8^2 = 64 $$ $$ (a^7)^2 = a^{7 \times 2} = a^{14} $$ 7. **Combine the results:** $$ 64a^{14} $$ **Final answer:** $$64a^{14}$$ which corresponds to option C.