Question 981380
 h(x)=3sqrt(x+2)-6


Try {{{g(x)=x+2}}}.  
.
{{{f(x)=sqrt(x-6)}}}.
The intermediate step may be {{{f(g(x))=sqrt(g(x)-6)}}}.


Resolving the composition on {{{h(x)=-4/x^2+x-1}}}  will not work the way you want.  Maybe first convert to single rational expression?
{{{(-4+x^2-x)/x^2}}}
{{{(x^2-x-4)/x^2}}}
Still would need to let x be assigned g(x).
Maybe another tutor would see how to find g and g  for this one.