Solution:

The good which is more necessary or required, or has less substitutes tends to have less demand elasticity, as when price changes, the demand doesn't change much. Then, we can solve the given as follows:

a) Required textbooks or mystery novels:

As required textbooks are necessary for students, as reasoned above, mystery novels will have more elastic demand.

b) Beethoven recordings or classical music recordings in general:

Classic music recordings in general cover a bigger market, while Beethoven is a specific person, for whom preferences could change more easily. Thus, Beethoven recordings will have more elastic demand.

c) Subway rides during next six months or next 5 years:

Relative to a good for shorter period, the longer period provides more demand elasticity for the good, possibly due to availability of more substitutes or alternatives or change in preferences, or adjustments. Thus, subway rides during next 5 years will have more elastic demand as people could have their personal vehicles by then.

d) Root beer or water:

Among the two mentioned, clearly water is a necessity good, and so water will have less elastic demand and root beer will have more elastic demand.