To find which word fills in the blank properly we can test how both words sound when plugged into the sentence.
Here's the first sentence with the option a filled in the blank : <span>The faculty <em>decide </em>which classes will be offered at various times during the day.
Here's the second sentence with the option b filled in the blank : </span>The faculty <span><em>decides </em></span>which classes will be offered at various times during the day.
Based on which sounds grammatically correct, we call tell that the right answer is option b.