Final answer:
The correct matches are distances to planets via radar ranging, distances to the nearest stars via parallax, distances to nearby galaxies via Cepheid variable stars, and distances to stars in the Milky Way more than 2,000 ly away via redshift.
Step-by-step explanation:
In astronomy, different distance indicators are used to measure how far away celestial objects are. The matching of methods to the appropriate objects results in the following: distances to planets are most commonly measured by radar ranging, distances to the nearest stars are often found using parallax, distances to nearby galaxies can be determined by observing Cepheid variable stars, and distances to stars in the Milky Way more than 2,000 light-years (ly) away are usually gauged using the redshift of their light. Therefore, the correct answer to the student's question is: Distances to planets via radar ranging, distances to the nearest stars via parallax, distances to nearby galaxies via Cepheid variable stars, and distances to stars in the Milky Way more than 2,000 ly away via redshift.