1. **State the problem:** We know that $\frac{3}{8}$ of the rectangle is shaded, and the shaded area is 72 m$^2$. The width of the rectangle is 12 m. We need to find the height of the rectangle. 2. **Write the formula for the area of a rectangle:** $$\text{Area} = \text{width} \times \text{height}$$ 3. **Express the shaded area in terms of the total area:** Since $\frac{3}{8}$ of the rectangle is shaded, $$\text{Shaded area} = \frac{3}{8} \times \text{Total area}$$ 4. **Set up the equation using the given shaded area:** $$72 = \frac{3}{8} \times (12 \times h)$$ where $h$ is the height of the rectangle. 5. **Solve for $h$:** Multiply both sides by $\frac{8}{3}$ to isolate $12h$: $$72 \times \frac{8}{3} = \cancel{\frac{3}{8}} \times \frac{8}{3} \times 12h$$ $$72 \times \frac{8}{3} = 12h$$ Calculate the left side: $$72 \times \frac{8}{3} = 72 \times \frac{8}{3} = 72 \times 2.6667 = 192$$ So, $$192 = 12h$$ 6. **Divide both sides by 12 to solve for $h$:** $$\frac{192}{\cancel{12}} = \frac{12h}{\cancel{12}}$$ $$16 = h$$ **Final answer:** The height of the rectangle is $16$ meters.