Astar that is several thousand times brighter than the sun with a temperature lower than 4,000 k would be classified as — a a main-sequence star in spectral class b b a supergiant in spectral class k c a main-sequence star in spectral class k or m d a white dwarf in spectral class b

B. a super-giant in spectral class K

Explanation:

The classification of stars are done on various characteristics like surface temperature, luminosity, spectral class etc. HR diagram is a plot which shows the relation between these characteristics of stars. One can also predict the life cycle of stars. When you plot the stars basis these characteristics on HR Diagram you can easily see that the stars with temperature lower than 4000K and brightness several thousand of that of the Sun will be a supergiant star.