1. **State the problem:** Solve for the variable in the proportion $\frac{20}{7} = \frac{6}{m}$. 2. **Formula used:** In a proportion $\frac{a}{b} = \frac{c}{d}$, the cross products are equal, so $a \times d = b \times c$. 3. **Apply the cross multiplication:** $$20 \times m = 7 \times 6$$ 4. **Simplify the right side:** $$20m = 42$$ 5. **Solve for $m$ by dividing both sides by 20:** $$m = \frac{42}{20}$$ 6. **Simplify the fraction:** $$m = \frac{21}{10} = 2.1$$ 7. **Answer:** The value of $m$ is $2.1$.