Answer
It takes $~~1.7\times 10^8~years~~$ for the Sun to make one revolution.
Work Step by Step
We can express the distance to the center of the Milky Way in units of $km$:
$r = (2.3\times 10^4~ly)(\frac{9.461\times 10^{12}~km}{1~ly}) = 2.176\times 10^{17}~km$
We can find the time it takes for the Sun to make one revolution:
$t = \frac{2\pi~r}{v}$
$t = \frac{(2\pi)(2.176\times 10^{17}~km)}{250~km/s}$
$t = 5.469\times 10^{15}~s$
$t = (5.469\times 10^{15}~s)(\frac{1~yr}{365\times 24\times 3600~s})$
$t = 1.7\times 10^8~yr$
It takes $~~1.7\times 10^8~years~~$ for the Sun to make one revolution.
