Astar’s light is shifted to the blue part of the light spectrum. what does this mean about the length of light waves and movement of the star?

a. the wavelengths are getting longer, meaning the star is moving away from the observer.

b. the wavelengths are getting longer, meaning the star is moving toward the observer.

c. the wavelengths are getting shorter, meaning the star is moving toward the observer.

d. the wavelengths are getting shorter, meaning the star is moving away from the observer.

A is the question that's that that's your question

The best way to describe doppler shift (or doppler effect, which this essentially is) so you can understand it is by comparing it to when you hear an ambulance or a train moving towards you. 
As it moves towards you, the pitch of the sound (the frequence) get's higher and higher, untill it passes you, and then the sound get's dimmer and dimmer. 

It's the same thing with light - when stars are moving away (red shift) the wavelenght increases and thus the object looks more redish (Because red colour has longer wavelenghts). As opposed to when the star is moving closer the wavelenght contracts (blue shift) and the object appears slightly blue.