Engine sputtering

I would check the condition of the plugs. Check the resistance on the plug wires. Have the computer scanned for codes. Check the fuel pressure under load. When was the last time you ran some fuel system conditioner/cleaner though it?

Never, my son just bought this car yesterday for $1,000.00, it does have an oil leak most likely needs a new valve cover gasket. Could that be causing the sputter? I am not trained in any way, when you say check the pressure I am assuming there is some sort of tool to use?

auto parts rent the gauge and you hook it to the fuel rail to check pressure.
https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

Great! Thank you for linking the guide.

I have not had time to check the pressure yet but while I was cleaning up the engine bay with some towels I notice a short hose (not sure what it goes to) is not all the way on and I could hear air coming from it while the engine was running. It is near the top only about an inch and a half long. Could it be related. Hear is a picture. I do not know if you can tell what it is. It is right at the end of that spring.

it is probably a vacuum leak. replace the hose or reconnect it and the sputtering should go away.