1. **State the problem:** We have two similar triangles, EFG and HIJ. We know sides GE = 8, EF = 3.6 in triangle EFG, and side JH = 24 in triangle HIJ. We need to find the length of side HI. 2. **Recall the property of similar triangles:** Corresponding sides of similar triangles are proportional. This means: $$\frac{GE}{JH} = \frac{EF}{HI}$$ 3. **Set up the proportion:** Using the given sides, $$\frac{8}{24} = \frac{3.6}{HI}$$ 4. **Simplify the left fraction:** $$\frac{\cancel{8}}{\cancel{24}} = \frac{1}{3}$$ 5. **Rewrite the proportion:** $$\frac{1}{3} = \frac{3.6}{HI}$$ 6. **Cross multiply to solve for $HI$:** $$1 \times HI = 3 \times 3.6$$ $$HI = 10.8$$ 7. **Answer:** The length of side $HI$ is $10.8$ units.