1. **State the problem:** We are given the equation $$\frac{4}{9} = \frac{8}{3} m$$ and need to find the value of $m$. 2. **Write the formula and explain:** To solve for $m$, we want to isolate $m$ on one side of the equation. We can do this by dividing both sides by $$\frac{8}{3}$$ or equivalently multiplying both sides by its reciprocal $$\frac{3}{8}$$. 3. **Isolate $m$:** $$ m = \frac{\frac{4}{9}}{\frac{8}{3}} = \frac{4}{9} \times \frac{3}{8} $$ 4. **Simplify the multiplication:** $$ m = \frac{4 \times 3}{9 \times 8} = \frac{12}{72} $$ 5. **Simplify the fraction by dividing numerator and denominator by 12:** $$ m = \frac{\cancel{12}^1}{\cancel{72}^6} = \frac{1}{6} $$ 6. **Final answer:** $$ m = \frac{1}{6} $$