Step 1 :Substitute \(g(x)\) into \(h(x)\) to get \(h(g(x))=f(g(g(x)))=\frac{1}{(g(x)-2)^{4}}\)
Step 2 :Substitute \(x-2\) for \(g(x)\) in the equation to get \(f(g(g(x)))=\frac{1}{((x-2)-2)^{4}}\)
Step 3 :Simplify the equation to get \(f(g(g(x)))=\frac{1}{(x-4)^{4}}\)
Step 4 :So, the function we are looking for is \(f(x)=\frac{1}{(x-4)^{4}}\)
Step 5 :Check our result by substituting \(g(x)\) into \(f(x)\) to see if we get \(h(x)\)
Step 6 :We get \(f(g(x))=\frac{1}{((x-2)-4)^{4}}=\frac{1}{(x-2)^{4}}=h(x)\)
Step 7 :So, our result is correct, and the final answer is \(\boxed{f(x)=\frac{1}{(x-4)^{4}}}\)