Answer
The orbital period of Vulcan would be 48 days.
Work Step by Step
Let $P_V$ be Vulcan's period.
Let $R_V$ be Vulcan's orbital radius.
Let $P_M$ be Mercury's period.
Let $R_M$ be Mercury's orbital radius.
We can use Kepler's third law to find Vulcan's period.
$(\frac{P_V}{P_M})^2 = (\frac{R_V}{R_M})^3$
$P_V = P_M~(\frac{R_V}{R_M})^{3/2}$
$P_V = (88~days)~(\frac{2R_M/3}{R_M})^{3/2}$
$P_V = (88~days)~(\frac{2}{3})^{3/2}$
$P_V = 48~days$
The orbital period of Vulcan would be 48 days.