1. **Problem Statement:** We have two similar triangles ABC and DEF. Given sides are $AB=3$ cm, $BC=4$ cm, and $DE=6$ cm. We need to find the length of side $EF$. 2. **Formula and Concept:** Since the triangles are similar, corresponding sides are proportional. This means: $$\frac{AB}{DE} = \frac{BC}{EF}$$ 3. **Substitute Known Values:** $$\frac{3}{6} = \frac{4}{EF}$$ 4. **Solve for $EF$:** Cross-multiply: $$3 \times EF = 6 \times 4$$ $$3EF = 24$$ Divide both sides by 3: $$EF = \frac{24}{3} = 8$$ 5. **Answer:** The length of side $EF$ is 8 cm. This uses the property of similar triangles where corresponding sides have equal ratios, allowing us to find the unknown side by setting up a proportion.