Find the direct object.
Chief Joseph wanted equality for his people
The direct object would be "wanted" right? Since it technically receives the action of the verb.
The word "wanted" IS the verb.
Chief Joseph [subj] wanted [v] _____.
The one word that goes in the blank is the direct object.
Actually, in the sentence "Chief Joseph wanted equality for his people," there isn't a direct object. The verb "wanted" is an intransitive verb, which means it does not require a direct object to complete its meaning.
A direct object is a noun, pronoun, or noun phrase that directly receives the action of a transitive verb. For example, in the sentence "She bought a car," the direct object is "car" because it directly receives the action of the verb "bought."
In your sentence, "equality for his people" is a prepositional phrase that functions as the object of the verb "wanted." It doesn't directly receive the action of the verb, but rather clarifies what Chief Joseph wanted.