Either the box picked by Alice at the first attempt may have had the prize or may not have had the prize, there are two event here.
Event $E1$: Alice picked the box with the prize on the first attempt which has a probability of $3/7$.
Now on the second attempt, she has a $2/5$ probability of winning the prize.
Event $E2$: Alice didn't pick the box with the prize on the first attempt which has a probability of $4/7$.
Now on the second attempt, she has a $3/5$ probability of winning the prize.
The probability of winning prize $P(W)$ is given as
$P(W) = P(E1)P(W/E1) + P(E2)P(W/E2)$
$=\left ( 3/7\right )*\left(2/5\right) + \left ( 4/7 \right )*\left ( 3/5 \right )$ = $18/35$
Hence, option D is the correct answer.