Question 135260
I'm presuming that you meant: {{{f(x) = -x^2 + 2x + 3}}} and {{{g(x) = (x-2)^2}}}


{{{g(f(x))=((f(x))-2)^2=(f(x))^2-4(f(x))+4}}}


Just substitute {{{-x^2 + 2x + 3}}} everywhere you see {{{f(x)}}} in  {{{(f(x))^2-4(f(x))+4}}} and start multiplying.  Take care with your signs.  Remember a minus sign distributes across parentheses when you remove any parentheses. Collect your like terms and you are done.