The distance from Earth to an object is unrelated to the speed at which that object is travelling.
Your question is the equivalent of asking "A car is travelling at a a speed of 50 mph, how far away is it from my house?"
No Regulus or Alpha Leonis is 23.8 parsecs from the Earth.
11 parsecs
260 +/- 20 parsecs.
The Earth orbits the Sun. The Sun orbits the common center of mass of the Milky Way galaxy as a whole, and it carries the Earth along with it. The Milky Way is moving in the general direction of the Andromeda galaxy, and both of them, and the other galaxies in the Local Group (and beyond, to a distance of about 60 million parsecs) are moving towards the Great At tractor.
Approx 260 +/- 20 parsecs.
The distance from Earth is about 6,500 light years (2000 parsecs).
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The Earth is in the MilkyWay galaxy.
The distance is 41 parsecs (approx 134 lightyears).
a) Earth is not a star, but a planet. b) Earth is not part of "another galaxy", but of our own galaxy.
Parsec is a unit of distance, arcseconds of angle, so in principle, the two can't be converted. However, if an object has a parallax of 5 milliarcseconds (0.005 arc-seconds), the distance in parsecs, from Earth, would be 1 / 0.005 = 200 parsecs.
It is within the Orion-Cygnus Arm, a spur towrds the outer edge of the galaxy. The solar system (and Earth) is located close to the inner rim in the Local Bubble, about half-way along the Arm's length, approximately 8,000 parsecs (26,000 light-years) from the galactic center.