Each side of a 30 -sided polygon has one of three lengths. The number of sides

Choice B is correct. It’s given that each side of a $30$-sided polygon has one of three lengths. It's also given that the number of sides with length $8$ $\text{centimeters} \left(\text{cm}\right)$ is $5$ times the number of sides $n$ with length $3 \text{cm}$. Therefore, there are $5\times n$, or $5n$, sides with length $8 \text{cm}$. It’s also given that there are $6$ sides with length $4 \text{cm}$. Therefore, the number of $3 \text{cm}$, $4 \text{cm}$, and $8 \text{cm}$ sides are $n$, $6$, and $5n$, respectively. Since there are a total of $30$ sides, the equation $n+6+5n=30$ represents this situation. Combining like terms on the left-hand side of this equation yields $6n+6=30$. Therefore, the equation that must be true for the value of $n$ is $6n+6=30$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.