So my son bought an 06 rx8 6 port 6 speed .Holly smokes its super fun , then it died with 117000 km
so had a new motor installed and just does not want to run right at low RPM but when you get to 6000 RPM runs fine
i have done a lot of work on it ,but what does the senser on the intake manifold right beside the oil filler neck do?

 

Some common mistakes when installing a new engine are mixing up injector wiring and mixing up coil to spark plug wiring. Simple things to check.

Around 5700rpm is where the SSV (intake secondaries) open, so if the SSV is stuck open your car will be unhappy below that range. You can move the SSV by hand to verify. If it doesn't move, it's stuck. The actuator is to the passenger side from the oil filler neck (assuming the car has the driver on the left). Simple fix if so, search here for SSV DIY.

The only thing I can think that looks like a sensor near the oil filler neck is the purge solenoid. It's an emissions thing, don't think it's hurting you right now. You might want to put up some pictures.

Are there any engine codes? Do you have an OBD2 reader to see what the fuel trims are like at idle and under 6k? It could be as simple as a vacuum leak, but we're guessing without that info.

 

Fixed it it was a red injector the wire was broken
i tested everything checked and double checked never seen that coming