So when stepping on the gas my car won't accelerate the engine revs but it does accelerate until trying after a few times than it will go normal until I slow down or stop than it starts over again ..

Check the clutch

Had that problem with my mercury sable after changing transmission if you would accelerate slow no problem but if you would accelerate fast would act like it is bogging down until you let off the gas and it would go back normal. The shift control solinold was bad easy fix mounts on the outside of transmission and shift cable goes to it.

Thanks guys hope I can figure It out soon

Also check the transmission fluid level.

Is this vehicle a manual or automatic transmission ?

Automatic. Mines a 2001 taurus se and it won't go past 60mph very rarely if any.

What is this called apparently it powers the transmission I accidentally broke some pins inside it and it put codes up for shift solenoids a b and c and said they were malfunctioning and after that it wouldn’t shift out of first but it would get up to speed fine and my car is a 1997 Ford Taurus GL and I want to know if that connector can be replaced

Yes it can you just have to make sure all wires are connected with the same color. Dont leave no wire cooper opened cover all wires while to make sure each wire has a tight connection.

Why does my 04 Taurus keep accelerating after letting up on the throttle? Had it diagnosed a couple times, but know one has an answer. Checked my cruise control cable and it seems fine