My car is a honda accord 1992 and the engine is not receiving engine coolant but at the same time it is spitting it out from the reservoir

Faulty radiator cap--doesn't maintain proper pressure or one or more valves are bad. Test cap relief pressure with a radiator cap tester (KD 3700 or Stant 12270). On non-expansion tank systems, such as on Hondas, there are two valves inside the cap that can fail. One allows hot coolant to flow into the overflow tank, the other allows coolant to flow from the overflow tank to the radiator, as the engine cools. If the coolant can't flow back into the engine, there won't be enough coolant and the engine can overheat. It's best to use a high quality, preferably OEM, cap.

Make sure the system has been bled. Many Hondas have radiators that are below the engine and need bleeding before coolant will circulate.