Step 1 :The question is asking for the value of the function \(f(x)\) at \(x+h\). To find this, we need to substitute \(x+h\) into the function and simplify the result.
Step 2 :Substitute \(x+h\) into the function \(f(x) = -3x + 6\) to get \(f(x+h) = -3(x+h) + 6\).
Step 3 :Simplify the expression to get \(f(x+h) = -3h - 3x + 6\).
Step 4 :Final Answer: \(f(x+h) = \boxed{-3h - 3x + 6}\)