1. **State the problem:** We have two similar rectangular prisms. The larger prism has a height of 12 cm and a base edge of 3 cm. The smaller prism has a base edge of 2 cm and an unknown height $x$ cm. We need to find $x$. 2. **Formula and rules:** For similar solids, corresponding linear dimensions are proportional. This means the ratio of heights equals the ratio of corresponding base edges: $$\frac{\text{height}_1}{\text{height}_2} = \frac{\text{base}_1}{\text{base}_2}$$ 3. **Set up the proportion:** $$\frac{12}{x} = \frac{3}{2}$$ 4. **Solve for $x$:** Cross multiply: $$12 \times 2 = 3 \times x$$ $$24 = 3x$$ 5. **Divide both sides by 3:** $$\frac{24}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$8 = x$$ 6. **Answer:** The missing height is $8$ cm.