1. **State the problem:** We have a 30-sided polygon with sides of three different lengths: 3 cm, 8 cm, and 4 cm. 2. The number of sides with length 8 cm is 5 times the number of sides with length 3 cm, which we call $n$. 3. There are 6 sides with length 4 cm. 4. We want to find the equation that correctly represents the total number of sides, which is 30. 5. The total number of sides is the sum of sides of length 3 cm, 8 cm, and 4 cm: $$n + 5n + 6 = 30$$ 6. Simplify the left side: $$6n + 6 = 30$$ 7. This matches option B. **Final answer:** The correct equation is $6n + 6 = 30$ (option B).