The force needed to accelerate an object varies directly with its acceleration. If a force of 24 newtons produces an acceleration of 6…

Direct variation means $F=ka$. From $24=k(6)$, the constant is $k=4$. When $a=10$, the force is $F=4(10)=40$ newtons, choice J. Equivalently, $\frac{24}{6}=\frac{F}{10}$ gives $F=40$. Choice F ($34$) adds $10$ to $24$ instead of scaling. Choice H ($44$) adds $20$ to $24$. Choice G ($60$) multiplies $6$ by $10$, which is the product of the two accelerations and has no physical meaning here. Direct variation is multiplicative: the ratio of force to acceleration stays constant at $4$.