sat-dog

Choice B is correct. Multiplying both sides of the given equation by $\left(3\right)\left(13\right)$, or $39$, yields $\left(39\right)\left(\frac{x+6}{3}\right)=\left(39\right)\left(\frac{x+6}{13}\right)$, or $13\left(x+6\right)=3\left(x+6\right)$. Subtracting $3\left(x+6\right)$ from both sides of this equation yields $10\left(x+6\right)=0$. Dividing both sides of this equation by $10$ yields $x+6=0$. Therefore, if $\frac{x+6}{3}=\frac{x+6}{13}$, then the value of $x+6$ is $0$. It follows that of the given choices, the value of $x+6$ is between $-2$ and $2$.

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.