Question

Which word in the sentence is a direct object? Nathan bought a sweater at the shopping mall

Answer 1

this might actually help you check this link out. http://www.grammar-monster.com/glossary/direct_object.htm

Answer 2

If you break down the sentence it is generally easier. So:
Nathan is the subject noun, bought is the predicate. Common stuff. The direct object refers to who or what is being given the action. The prepositional phrase "at the shopping mall" tells where. You should be able to figure that out! Hope I helped :)