$\textbf{Answer:}$

$y=24 x-79$

$\textbf{Explanation:}$

Find the slope of the tangent line:

$m_t = f ' (x)$

$m_t = 6x|_{x=4}$

$ m_t = 6(4)$

$ m_t =24$

Find the points where the tangent line touches the function

We know $x=4$

$f(x) = 3x^2 - {\pi}^3$

$\implies f(4) = 3(4)^2 - {\pi}^3$

$ \implies f(4) \approx 17 =y$

we now have $ (x_1,y_1) = (4,17)$

Now, use the point-slope formula to find the equation,

$y-y_1 = m_t(x-x_1)$

$y -17 = 24(x-4)$

$ y-17 = 24x-96$

$ y=24x-79$