Answer
The sun is moving at a speed of $199~km/s$ with respect to the center of the galaxy.
Work Step by Step
We can find the sun's linear speed as it orbits around the center of the galaxy:
$v = \frac{d}{t}$
$v = \frac{2\pi~r}{t}$
$v = \frac{(2\pi)(2\times 10^{20}~m)}{(2.0\times 10^8)(365)(24)(3600~s)}$
$v = 199,000~m/s$
$v = 199~km/s$
The sun is moving at a speed of $199~km/s$ with respect to the center of the galaxy.
