"Crystal could hear her sister snoring across the room."
Who's/who is performing/doing something/ some action?
Crystal is. Therefore Crystal is the subject.
What is the action, what is being done?
Crystal was listening and could hear something. So, 'could hear' tells us what action is happening. It is the verb.
"could hear" whom or what?
She could hear 'her sister', so this is the object.