She forgot about the final x at the end, because the first expression is 3x+6+x, and the second one is 3(x+2). The second one expands to 3x+6, but it doesn't have the final term at the end.
Also, 3 is not really a factor of x (technically it could be because x in unknown, but in terms of like terms and stuff it isn't) so you can't take a 3 out of x (unless you leave it as 1/3x I guess).
Anyway, yeah she forgot about the final x and therefore the factor she took out is incorrect anyway. She also could've simplified the first expression so that it became 4x + 6
