Step 1 :The function \((g \circ f)(x)\) represents the composition of the functions \(g\) and \(f\), which means we substitute \(f(x)\) into \(g(x)\). So, we need to substitute \(f(x)=-6x+4\) into \(g(x)=2x+3\).
Step 2 :Substitute \(f(x)\) into \(g(x)\) to get \(g(f(x)) = 2(-6x+4) + 3\).
Step 3 :Simplify the expression to get \(g(f(x)) = -12x + 8 + 3\).
Step 4 :Further simplify the expression to get \(g(f(x)) = -12x + 11\).
Step 5 :Final Answer: The composition of the functions \(g\) and \(f\) is \((g \circ f)(x) = -12x + 11\), so the correct answer is \(\boxed{-12x + 11}\).