1. **State the problem:** We have two similar triangles ABC and DEF. Given sides $AB=3$ cm, $BC=4$ cm, and $DE=6$ cm, we need to find the length of side $EF$. 2. **Recall the property of similar triangles:** Corresponding sides of similar triangles are proportional. This means: $$\frac{AB}{DE} = \frac{BC}{EF}$$ 3. **Set up the proportion:** Substitute the 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.