I just recently change the transmission fluid in my 96 gt 4.6l and I put it back together and now my shifter wants to go to the right I had to force it to the left what can be the problem

 

Define "put it back together".
How does draining and filling the transmission require any dis-assembly?
I assume manual trans because you said the shifter want to go to the right.

 

When I reinstalled the shifter I put the bushing or plastic cupping back on and everything like I was supposed to and now the shifter just wants to go to the right when its in neutral just go straight to the right I have to force it to the left and into first and second

 

automatic?

manual?

what did you take apart to change fluid?

 

It’s a manual and I took shifter out to change the fluid I put it back same way I took it out and now it wants to stay to right and hard to go in 1 & 2 I took it back out to double check make sure now grit or dirt anything was in there and still same thing

 

Something changed from before when you removed the shifter. So you are going to have to take a closer look at what you changed. Maybe take pictures if you take it apart again so we can see what it is exactly that you are doing, or have done.