1 3 x + 6 - 1 2 x + 6 = - 8 What value

The correct answer is $42$. The expression $\left(x+6\right)$ is a factor of both terms on the left-hand side of the given equation. Therefore, the given equation can be written as $\left(x+6\right)\left(\frac{1}{3}-\frac{1}{2}\right)=-8$, or $\left(x+6\right)\left(-\frac{1}{6}\right)=-8$. Multiplying each side of this equation by $-6$ yields $x+6=48$. Subtracting $6$ from each side of this equation yields $x=42$. Therefore, the value of $x$ that is the solution to the given equation is $42$.