The variable y varies inversely with x. If y = 8 when x = 3, what is y when x = 6?

Inverse variation means $y=\frac{k}{x}$, so the product $xy$ stays constant. From the given values, $k=8\cdot3=24$. When $x=6$, $y=\frac{24}{6}=4$, choice G. Doubling $x$ from $3$ to $6$ cuts $y$ in half, from $8$ to $4$. Choice F ($16$) treats the relationship as direct variation, doubling $y$ when $x$ doubles. Choice H ($2$) divides $y$ by $4$, dividing twice instead of once. Choice J ($24$) reports the constant $k$ itself instead of the value of $y$. A quick check: $6\cdot4=24=3\cdot8$, so the product is unchanged.