There seems to be insufficient information because f(x) hasn’t been defined.
For example, if g(x)=x²-11, then f(x)=2x, and g(2)=4-11=-7, so g(4)=16-11=5.
But, if g(x)=1-x³, then f(x)=-3x², and g(2)=-7, so g(4)=1-64=-63. Note that f(x) is redundant because it’s not involved in determining g(4).
And many more examples could be cited, so there is no unique answer.