1. **State the problem:** We need to make $a$ the subject of the formula given by $$b^3 = \frac{4(8d - 3a)}{9}$$ 2. **Isolate the fraction:** Multiply both sides by 9 to eliminate the denominator: $$9b^3 = 4(8d - 3a)$$ 3. **Expand the right side:** $$9b^3 = 32d - 12a$$ 4. **Rearrange to isolate terms with $a$:** Move $32d$ to the left side: $$9b^3 - 32d = -12a$$ 5. **Divide both sides by $-12$ to solve for $a$:** $$a = \frac{32d - 9b^3}{12}$$ 6. **Final answer:** $$a = \frac{32d - 9b^3}{12}$$ This expresses $a$ in terms of $b$ and $d$ clearly and correctly.