If $f(2x-3) = 4x-2$, then what is $f(x)$? I have this statement: 

If $f(2x-3) = 4x-2,$ the function $f(x)$ is ...?

My attempt was:
Move the function $3$ units to the left
$f(2x) = 4(x+3) -2 = 4x+10$
Divide $x$ by $2$
$f(x) = 2x+10$
Verifiy $f(x) = 2x+10 \to f(2x) = 4x+10 \to f(2x-3) = 4(x-3)+10 = \underbrace{4x-2}_{f(2x-3)}$
But according to the  guide the correct answer is $2x+4$ and i don't know why. Thans in advance.

Correct answer:
Let $y=2x-3$.  Then $f(y)=4x-2=2(2x-3)+4=2y+4.$
Where you went wrong:
If $f(2x-3)=4x-2=2(2x)-2$, then $f(2x)=2(2x+3)-2=4x+4.$
