Let $f(x)=x-2$ and $g(x)=4^{x}$.
a. Evaluate each of the following.
i. $f(g(3))=$ $\mathrm{T}$
Enter a mathematical
ii. $g(f(6))=$

Step 1 ：Let \(f(x)=x-2\) and \(g(x)=4^{x}\).

Step 2 ：We need to evaluate \(f(g(3))\) and \(g(f(6))\).

Step 3 ：To find \(f(g(3))\), first find the value of \(g(3)\).

Step 4 ：Substitute \(x=3\) into \(g(x)\) to get \(g(3)=4^{3}=64\).

Step 5 ：Then substitute \(g(3)=64\) into \(f(x)\) to get \(f(g(3))=64-2=62\).

Step 6 ：So, \(f(g(3))=\boxed{62}\).

Step 7 ：To find \(g(f(6))\), first find the value of \(f(6)\).

Step 8 ：Substitute \(x=6\) into \(f(x)\) to get \(f(6)=6-2=4\).

Step 9 ：Then substitute \(f(6)=4\) into \(g(x)\) to get \(g(f(6))=4^{4}=256\).

Step 10 ：So, \(g(f(6))=\boxed{256}\).