1. **State the problem:** We need to find how much space should be allowed for 48 seedlings if 64 seedlings require 24 cm\textsuperscript{2} of space. 2. **Identify the relationship:** The space allowed is directly proportional to the number of seedlings. This means: $$\frac{\text{space}_1}{\text{seedlings}_1} = \frac{\text{space}_2}{\text{seedlings}_2}$$ 3. **Write the formula:** Let $x$ be the space allowed for 48 seedlings. $$\frac{24}{64} = \frac{x}{48}$$ 4. **Solve for $x$:** Multiply both sides by 48: $$x = \frac{24}{64} \times 48$$ 5. **Simplify the fraction:** $$x = 24 \times \frac{\cancel{48}}{64} \times \cancel{1} = 24 \times \frac{3}{4}$$ 6. **Calculate the value:** $$x = 24 \times 0.75 = 18$$ 7. **Answer:** The space allowed for 48 seedlings should be 18 cm\textsuperscript{2}.