Question

Classify the subordinate clause as a noun, adjective, or adverb clause. Indicate whether it is introduced by a relative pronoun, a subordinating conjunction, or neither. The men quit work when the whistle blew.

Answer 1

Let's start a little further back
Men is the subject of the main clause. 
The is an article modifying men. The is a specific set of men.
quit is a verb. It provides the action. 
work is a noun. It is the object of the sentence.

Now we can get to what you really want to know. The reason to go back to the main clause is that you have to pick a word that the subordinate conjunction connects to. 

Take the whole clause. "when the whistle blew." 
Just what does it do?
Does it modify quit or does it modify work Or does it modify men?

If it modifies men, then what kind of men are when the whistle blew? Since that makes no sense, when the whistle blew is not an adjective modifying men.

If modifies work, we ask the same question. What kind of work is when the whistle blew? Again, when the whistle blew is not an adjective for describing work.

There is only one choice left. Does it modify quit. Yes because it tells when the quitting took place.
When the whistle blew is an adverb clause.
(modifying quit) <<<<<<< answer

When is a subordinating conjunction <<<<< answer