What can I do if my direct report and my boss give me different directions?

Punt - this is a no win situation.

Why are you taking directions from your direct report? Or perhaps you mean that your boss is giving your direct report different direction than they are giving you? If that's the case, just clarify it with your boss. Unless your boss is problematic or Machiavellian, most people do things like this unintentionally. Perhaps your direct report misunderstood something. Or maybe your boss left out some necessary context with the direct report in an effort to simplify. A call or meeting with the three of you will clear this up in a few minutes If necessary, set up a meeting with your boss and direct report to go over whatever it is together. Tell your boss that you have questions and then invite your direct report.

Personally, I would speak with both of them to gain clarity.

If it's relevant to your job description, follow. If not, ask, if unethical, discuss, all fails, talk to a boss above, if not, talk to HR.

Listen to your boss. Why would you care if your direct report is saying something else if the person who controls whether or not you have a job is saying something different? It's one thing if YOU don't agree with your boss - but you should never have to explain your boss' reasoning to your direct reports if you don't feel comfortable doing so.

A quick stand up meeting to clarify.

Talk to your direct report. Use the proper chain of command.

Communication is key; Talk to them together. Be diplomatic and don't throw anyone under the bus, but be up front with both parties: let them know you've been given conflicting directions and need clarification based on their consensus. Follow up the conversation with an email to everyone involved (it is a great form of documentation in which all parties can get on the same page to which you can refer back later).