It was OK until your last step.  However  
h(x) does NOT mean h times x, nor h∙x nor hx.
f(4) does NOT mean f times 4 nor 4∙f nor 4f.
g(2) does NOT mean g times 2 nor 2∙g nor 2g.

Unless you are given equations for f(x) and g(x),
the final answer is 2f(4)-g(2).  You stop there.

Although you were taught that f(x) means f times x
in first year algebra, in college algebra it does 
not mean multiplication!

In college algebra, a single letter with a parentheses 
just to the right of it usually means functional notation. 

f(x) is read "f of x".
f(4) is read "f of 4".
g(2) is read "g of 2".

If you were given equations, say, 

f(x) = 2x-3 

g(x) = 5x+1

h(x) = 2f(x+1)-g(x-1)

This is how you would proceed.

You would do what you did above:

h(3) = 2f(3+1)-g(3-1)
h(3) = 2f(4)-g(2)

But then you would find f(4) by substituting 
4 for x in the equation for f(x):

f(x) = 2x-3
f(4) = 2(3)-3 = 6-3 = 3

And then you would find g(2) by substituting 
2 for x in the equation for g(x):

g(x) = 5x+1
g(2) = 5(2)+1 = 10+1 = 11

And then substitute 3 for f(4) and 11 for g(2) in

h(3) = 2f(4)-g(2)
h(3) = 2(3)-11  
h(3) = 6-11
h(3) = -5

A number with a parentheses just after it DOES mean
multiplication in both first year algebra and college
algebra.  However when you see a letter with a parentheses
after it, such as f(x), g(x), or t(x), it usually 
means to substitute what is in the parentheses for 
x in the given equation for f(x), g(x), or t(x).

I realize this may get some getting used to.  

When you see a college algebra problem like this:

Given f(x) = 4x-3, find f(7),

it is the same problem as the first year algebra problem:

Given y = 4x-3, find y when x = 7.

The answer to both problems would be 25.

Hope this helps you.

Edwin