Q: My 2013 Ram 2500 will not go into 4th, 5th, or 6th gear, when it tries to go into 4th gear it does not do anything

Your vehicle was equipped with Chrysler’s 66RFE transmission. This transmission model has not been hugely problematic and I do not see many reports of the type of failure you are describing. I see only one similar report of shift failure, from fourth onward, in the NHTSA database. There is a pretty involved diagnostic decision tree, covering many, many pages, for this shift failure on your model. The solenoids are a possibility and hopefully the problem will be found with a component such as that or the electronic controls. All other causes are clutch and/or hydraulic circuit related and thus would require rebuilding the unit (not difficult though). To diagnose this yourself you will need the 66RFE manual. If you desire a diagnostic from a YourMechanic professional, the service to request is a transmission shift diagnostic. If you request that service, the responding certified mechanic will determine the root cause of the failure to shift. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.