2<2x+4<10

The answer I got is:

2>2x+4 or 2x+4<10

-2>2x or 2x<6

-1>x or x<3

Why did you flip the interval sign?

2<2x+4 to 2>2x+4

So I would leave the sign the way it was and is my answer correct?

yes, -1<x<3
you don't have to split into two parts. Just do the same thing to every portion.