The mp3 player that was least expensive was a big hit with the distance runners.
the adjective clause that was least expensive modifies
a)
the verb was.
b)
the noun runners.
c)
the noun mp3 player.
d)
the adjective distance.

The adjective clause "that was least expensive" modifies C.) THE NOUN MP3 PLAYER.

An adjective clause is recognized by the following criteria:
1) contains subject and verb
2) begins with relative pronoun or relative adverb - in this case, relative pronoun (that)
3) It functions as an adjective that answers the questions: what kind? how many? which one? - in this case, the question is: which one is the least expensive?

The adjective clause will follow only two patterns:
1) Relative pronoun or adverb + subject + verb
2) Relative pronoun as subject + verb

In this case, the adjective clause followed the second pattern: "that" is the relative pronoun as subject and "was" as the verb.