Given $f(3)=6$ and $f^{\prime}(3)=13$, find the value of $h^{\prime}(3)$ based on the function below.
\[
h(x)=(-3 x+4) \cdot f(x)
\]

Step 1 ：We are given the function \(h(x)=(-3 x+4) \cdot f(x)\) and we are asked to find the derivative of this function at \(x=3\).

Step 2 ：We can use the product rule for differentiation, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.

Step 3 ：In this case, the two functions are \(-3x+4\) and \(f(x)\).

Step 4 ：Let's denote \(f(x)\) as \(f\) and its derivative as \(f'\).

Step 5 ：Applying the product rule, we get \(h'(x) = (-3x+4)f'(x) - 3f(x)\).

Step 6 ：We are given that \(f(3)=6\) and \(f'(3)=13\). Substituting these values into the equation, we get \(h'(3) = (-3*3+4)*13 - 3*6 = -83\).

Step 7 ：So, the value of \(h'(3)\) is \(\boxed{-83}\).